var.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
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/*  Copyright (c) 2002-2024 Zuse Institute Berlin (ZIB)                      */
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/*  Licensed under the Apache License, Version 2.0 (the "License");          */
/*  you may not use this file except in compliance with the License.         */
/*  You may obtain a copy of the License at                                  */
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/*      http://www.apache.org/licenses/LICENSE-2.0                           */
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/*  Unless required by applicable law or agreed to in writing, software      */
/*  distributed under the License is distributed on an "AS IS" BASIS,        */
/*  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */
/*  See the License for the specific language governing permissions and      */
/*  limitations under the License.                                           */
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/*  You should have received a copy of the Apache-2.0 license                */
/*  along with SCIP; see the file LICENSE. If not visit scipopt.org.         */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   var.c
 * @ingroup OTHER_CFILES
 * @brief  methods for problem variables
 * @author Tobias Achterberg
 * @author Timo Berthold
 * @author Gerald Gamrath
 * @author Stefan Heinz
 * @author Marc Pfetsch
 * @author Michael Winkler
 * @author Kati Wolter
 * @author Stefan Vigerske
 *
 * @todo Possibly implement the access of bounds of multi-aggregated variables by accessing the
 * corresponding linear constraint if it exists. This seems to require some work, since the linear
 * constraint has to be stored. Moreover, it has even to be created in case the original constraint
 * was deleted after multi-aggregation, but the bounds of the multi-aggregated variable should be
 * changed. This has to be done with care in order to not loose the performance gains of
 * multi-aggregation.
 */

/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/

#include "scip/cons.h"
#include "scip/event.h"
#include "scip/history.h"
#include "scip/implics.h"
#include "scip/lp.h"
#include "scip/primal.h"
#include "scip/prob.h"
#include "scip/pub_cons.h"
#include "scip/pub_history.h"
#include "scip/pub_implics.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_misc_sort.h"
#include "scip/pub_prop.h"
#include "scip/pub_var.h"
#include "scip/relax.h"
#include "scip/set.h"
#include "scip/sol.h"
#include "scip/stat.h"
#include "scip/struct_event.h"
#include "scip/struct_lp.h"
#include "scip/struct_prob.h"
#include "scip/struct_set.h"
#include "scip/struct_stat.h"
#include "scip/struct_var.h"
#include "scip/tree.h"
#include "scip/var.h"
#include <string.h>

#define MAXIMPLSCLOSURE 100  /**< maximal number of descendants of implied variable for building closure
                              *   in implication graph */
#define MAXABSVBCOEF    1e+5 /**< maximal absolute coefficient in variable bounds added due to implications */


/*
 * Debugging variable release and capture
 *
 * Define DEBUGUSES_VARNAME to the name of the variable for which to print
 * a backtrace when it is captured and released.
 * Optionally define DEBUGUSES_PROBNAME to the name of a SCIP problem to consider.
 * Have DEBUGUSES_NOADDR2LINE defined if you do not have addr2line installed on your system.
 */
/* #define DEBUGUSES_VARNAME "t_t_b7" */
/* #define DEBUGUSES_PROBNAME "t_st_e35_rens" */
/* #define DEBUGUSES_NOADDR2LINE */

#ifdef DEBUGUSES_VARNAME
#include <execinfo.h>
#include <stdio.h>
#include <stdlib.h>
#include "scip/struct_scip.h"

/** obtains a backtrace and prints it to stdout. */
static
void print_backtrace(void)
{
   void* array[10];
   char** strings;
   int size;
   int i;

   size = backtrace(array, 10);
   strings = backtrace_symbols(array, size);
   if( strings == NULL )
      return;

   /* skip first entry, which is the print_backtrace function */
   for( i = 1; i < size; ++i )
   {
      /* if string is something like
       *  /path/to/scip/bin/../lib/shared/libscip-7.0.1.3.linux.x86_64.gnu.dbg.so(+0x2675dd3)
       * (that is, no function name because it is a inlined function), then call
       * addr2line -e <libname> <addr> to get func and code line
       * dladdr() may be an alternative
       */
      char* openpar;
      char* closepar = NULL;
#ifndef DEBUGUSES_NOADDR2LINE
      openpar = strchr(strings[i], '(');
      if( openpar != NULL && openpar[1] == '+' )
         closepar = strchr(openpar+2, ')');
#endif
      if( closepar != NULL )
      {
         char cmd[SCIP_MAXSTRLEN];
         (void) SCIPsnprintf(cmd, SCIP_MAXSTRLEN, "addr2line -f -p -e \"%.*s\" %.*s", openpar - strings[i], strings[i], closepar-openpar-1, openpar+1);
         printf("  ");
         fflush(stdout);
         system(cmd);
      }
      else
         printf("  %s\n", strings[i]);
    }

  free(strings);
}
#endif

/*
 * hole, holelist, and domain methods
 */

/** creates a new holelist element */
static
SCIP_RETCODE holelistCreate(
   SCIP_HOLELIST**       holelist,           /**< pointer to holelist to create */
   BMS_BLKMEM*           blkmem,             /**< block memory for target holelist */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Real             left,               /**< left bound of open interval in new hole */
   SCIP_Real             right               /**< right bound of open interval in new hole */
   )
{
   assert(holelist != NULL);
   assert(blkmem != NULL);
   assert(SCIPsetIsLT(set, left, right));

   SCIPsetDebugMsg(set, "create hole list element (%.15g,%.15g) in blkmem %p\n", left, right, (void*)blkmem);

   SCIP_ALLOC( BMSallocBlockMemory(blkmem, holelist) );
   (*holelist)->hole.left = left;
   (*holelist)->hole.right = right;
   (*holelist)->next = NULL;

   return SCIP_OKAY;
}

/** frees all elements in the holelist */
static
void holelistFree(
   SCIP_HOLELIST**       holelist,           /**< pointer to holelist to free */
   BMS_BLKMEM*           blkmem              /**< block memory for target holelist */
   )
{
   assert(holelist != NULL);
   assert(blkmem != NULL);

   while( *holelist != NULL )
   {
      SCIP_HOLELIST* next;

      SCIPdebugMessage("free hole list element (%.15g,%.15g) in blkmem %p\n", 
         (*holelist)->hole.left, (*holelist)->hole.right, (void*)blkmem);

      next = (*holelist)->next;
      BMSfreeBlockMemory(blkmem, holelist);
      assert(*holelist == NULL);

      *holelist = next;
   }
   assert(*holelist == NULL);
}

/** duplicates a list of holes */
static
SCIP_RETCODE holelistDuplicate(
   SCIP_HOLELIST**       target,             /**< pointer to target holelist */
   BMS_BLKMEM*           blkmem,             /**< block memory for target holelist */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_HOLELIST*        source              /**< holelist to duplicate */
   )
{
   assert(target != NULL);

   while( source != NULL )
   {
      assert(source->next == NULL || SCIPsetIsGE(set, source->next->hole.left, source->hole.right));
      SCIP_CALL( holelistCreate(target, blkmem, set, source->hole.left, source->hole.right) );
      source = source->next;
      target = &(*target)->next;
   }

   return SCIP_OKAY;
}

/** adds a hole to the domain */
static
SCIP_RETCODE domAddHole(
   SCIP_DOM*             dom,                /**< domain to add hole to */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Real             left,               /**< left bound of open interval in new hole */
   SCIP_Real             right,              /**< right bound of open interval in new hole */
   SCIP_Bool*            added               /**< pointer to store whether the hole was added (variable didn't had that hole before), or NULL */
   )
{
   SCIP_HOLELIST** insertpos;
   SCIP_HOLELIST* next;

   assert(dom != NULL);
   assert(added != NULL);

   /* search for the position of the new hole */
   insertpos = &dom->holelist;
   while( *insertpos != NULL && (*insertpos)->hole.left < left )
      insertpos = &(*insertpos)->next;

   /* check if new hole already exists in the hole list or is a sub hole of an existing one */
   if( *insertpos != NULL && (*insertpos)->hole.left == left && (*insertpos)->hole.right >= right )  /*lint !e777 */
   {
      SCIPsetDebugMsg(set, "new hole (%.15g,%.15g) is redundant through known hole (%.15g,%.15g)\n",
         left, right, (*insertpos)->hole.left, (*insertpos)->hole.right);
      *added = FALSE;
      return SCIP_OKAY;
   }

   /* add hole */
   *added = TRUE;

   next = *insertpos;
   SCIP_CALL( holelistCreate(insertpos, blkmem, set, left, right) );
   (*insertpos)->next = next;

   return SCIP_OKAY;
}

/** merges overlapping holes into single holes, computes and moves lower and upper bound, respectively */
/**@todo  the domMerge() method is currently called if a lower or an upper bound locally or globally changed; this could
 *        be more efficient if performed with the knowledge if it was a lower or an upper bound which triggered this
 *        merge */
static
void domMerge(
   SCIP_DOM*             dom,                /**< domain to merge */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Real*            newlb,              /**< pointer to store new lower bound */
   SCIP_Real*            newub               /**< pointer to store new upper bound */
   )
{
   SCIP_HOLELIST** holelistptr;
   SCIP_HOLELIST** lastnextptr;
   SCIP_Real* lastrightptr;

   assert(dom != NULL);
   assert(SCIPsetIsLE(set, dom->lb, dom->ub));

#ifndef NDEBUG
   {
      /* check if the holelist is sorted w.r.t. to the left interval bounds */
      SCIP_Real lastleft;

      holelistptr = &dom->holelist;

      lastleft = -SCIPsetInfinity(set);

      while( *holelistptr != NULL )
      {
         if( (*holelistptr)->next != NULL )
         {
            assert( SCIPsetIsLE(set, lastleft, (*holelistptr)->hole.left) );
            lastleft = (*holelistptr)->hole.left;
         }

         holelistptr = &(*holelistptr)->next;
      }   
   }
#endif

   SCIPsetDebugMsg(set, "merge hole list\n");

   holelistptr = &dom->holelist;
   lastrightptr = &dom->lb;  /* lower bound is the right bound of the hole (-infinity,lb) */
   lastnextptr = holelistptr;

   while( *holelistptr != NULL )
   {
      SCIPsetDebugMsg(set, "check hole (%.15g,%.15g) last right interval was <%.15g>\n", (*holelistptr)->hole.left, (*holelistptr)->hole.right, *lastrightptr);

      /* check that the hole is not empty */
      assert(SCIPsetIsLT(set, (*holelistptr)->hole.left, (*holelistptr)->hole.right));

      if( SCIPsetIsGE(set, (*holelistptr)->hole.left, dom->ub) )
      {
         /* the remaining holes start behind the upper bound: remove them */
         SCIPsetDebugMsg(set, "remove remaining hole since upper bound <%.15g> is less then the left hand side of the current hole\n", dom->ub);
         holelistFree(holelistptr, blkmem);
         assert(*holelistptr == NULL);

         /* unlink this hole from the previous hole */
         *lastnextptr = NULL;
      }
      else if( SCIPsetIsGT(set, (*holelistptr)->hole.right, dom->ub) )
      {
         /* the hole overlaps the upper bound: decrease upper bound, remove this hole and all remaining holes */
         SCIPsetDebugMsg(set, "upper bound <%.15g> lays in current hole; store new upper bound and remove this and all remaining holes\n", dom->ub);

         assert(SCIPsetIsLT(set, (*holelistptr)->hole.left, dom->ub));

         /* adjust upper bound */
         dom->ub = (*holelistptr)->hole.left;

         if(newub != NULL )
            *newub = (*holelistptr)->hole.left;

         /* remove remaining hole list */
         holelistFree(holelistptr, blkmem);
         assert(*holelistptr == NULL);

         /* unlink this hole from the previous hole */
         *lastnextptr = NULL;
      }
      else if( SCIPsetIsGT(set, *lastrightptr, (*holelistptr)->hole.left) )
      {
         /* the right bound of the last hole is greater than the left bound of this hole: increase the right bound of
          * the last hole, delete this hole */
         SCIP_HOLELIST* nextholelist;

         if( SCIPsetIsEQ(set, *lastrightptr, dom->lb ) )
         {
            /* the reason for the overlap results from the lower bound hole (-infinity,lb); therefore, we can increase
             * the lower bound */
            SCIPsetDebugMsg(set, "lower bound <%.15g> lays in current hole; store new lower bound and remove hole\n", dom->lb);
            *lastrightptr = MAX(*lastrightptr, (*holelistptr)->hole.right);

            /* adjust lower bound */
            dom->lb = *lastrightptr;

            if(newlb != NULL )
               *newlb = *lastrightptr;
         }
         else
         {
            SCIPsetDebugMsg(set, "current hole overlaps with the previous one (...,%.15g); merge to (...,%.15g)\n",
               *lastrightptr, MAX(*lastrightptr, (*holelistptr)->hole.right) );
            *lastrightptr = MAX(*lastrightptr, (*holelistptr)->hole.right);
         }
         nextholelist = (*holelistptr)->next;
         (*holelistptr)->next = NULL;
         holelistFree(holelistptr, blkmem);

         /* connect the linked list after removing the hole */
         *lastnextptr = nextholelist;

         /* get next hole */
         *holelistptr = nextholelist;
      }
      else
      {
         /* the holes do not overlap: update lastholelist and lastrightptr */
         lastrightptr = &(*holelistptr)->hole.right;
         lastnextptr = &(*holelistptr)->next;

         /* get next hole */
         holelistptr = &(*holelistptr)->next;
      }
   }

#ifndef NDEBUG
   {
      /* check that holes are merged */
      SCIP_Real lastright;

      lastright = dom->lb; /* lower bound is the right bound of the hole (-infinity,lb) */
      holelistptr = &dom->holelist;

      while( *holelistptr != NULL )
      {
         /* check the the last right interval is smaller or equal to the current left interval (none overlapping) */
         assert( SCIPsetIsLE(set, lastright, (*holelistptr)->hole.left) );

         /* check the hole property (check that the hole is not empty) */
         assert( SCIPsetIsLT(set, (*holelistptr)->hole.left, (*holelistptr)->hole.right) );
         lastright = (*holelistptr)->hole.right;

         /* get next hole */
         holelistptr = &(*holelistptr)->next;
      }   

      /* check the the last right interval is smaller or equal to the upper bound (none overlapping) */     
      assert( SCIPsetIsLE(set, lastright, dom->ub) );
   }
#endif
}

/*
 * domain change methods
 */

/** ensures, that bound change info array for lower bound changes can store at least num entries */
static
SCIP_RETCODE varEnsureLbchginfosSize(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(var != NULL);
   assert(var->nlbchginfos <= var->lbchginfossize);
   assert(SCIPvarIsTransformed(var));

   if( num > var->lbchginfossize )
   {
      int newsize;

      newsize = SCIPsetCalcMemGrowSize(set, num);
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &var->lbchginfos, var->lbchginfossize, newsize) );
      var->lbchginfossize = newsize;
   }
   assert(num <= var->lbchginfossize);

   return SCIP_OKAY;
}

/** ensures, that bound change info array for upper bound changes can store at least num entries */
static
SCIP_RETCODE varEnsureUbchginfosSize(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(var != NULL);
   assert(var->nubchginfos <= var->ubchginfossize);
   assert(SCIPvarIsTransformed(var));

   if( num > var->ubchginfossize )
   {
      int newsize;

      newsize = SCIPsetCalcMemGrowSize(set, num);
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &var->ubchginfos, var->ubchginfossize, newsize) );
      var->ubchginfossize = newsize;
   }
   assert(num <= var->ubchginfossize);

   return SCIP_OKAY;
}

/** adds domain change info to the variable's lower bound change info array */
static
SCIP_RETCODE varAddLbchginfo(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Real             oldbound,           /**< old value for bound */
   SCIP_Real             newbound,           /**< new value for bound */
   int                   depth,              /**< depth in the tree, where the bound change takes place */
   int                   pos,                /**< position of the bound change in its bound change array */
   SCIP_VAR*             infervar,           /**< variable that was changed (parent of var, or var itself) */
   SCIP_CONS*            infercons,          /**< constraint that inferred this bound change, or NULL */
   SCIP_PROP*            inferprop,          /**< propagator that deduced the bound change, or NULL */
   int                   inferinfo,          /**< user information for inference to help resolving the conflict */
   SCIP_BOUNDTYPE        inferboundtype,     /**< type of bound for inference var: lower or upper bound */
   SCIP_BOUNDCHGTYPE     boundchgtype        /**< bound change type: branching decision or inferred bound change */
   )
{
   assert(var != NULL);
   assert(SCIPsetIsLT(set, oldbound, newbound));
   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || SCIPsetIsFeasIntegral(set, oldbound));
   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || SCIPsetIsFeasIntegral(set, newbound));
   assert(!SCIPvarIsBinary(var) || SCIPsetIsEQ(set, oldbound, 0.0));
   assert(!SCIPvarIsBinary(var) || SCIPsetIsEQ(set, newbound, 1.0));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING || infervar != NULL);
   assert((boundchgtype == SCIP_BOUNDCHGTYPE_CONSINFER) == (infercons != NULL));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_PROPINFER || inferprop == NULL);

   SCIPsetDebugMsg(set, "adding lower bound change info to var <%s>[%g,%g]: depth=%d, pos=%d, infer%s=<%s>, inferinfo=%d, %g -> %g\n",
      SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, depth, pos, infercons != NULL ? "cons" : "prop",
      infercons != NULL ? SCIPconsGetName(infercons) : (inferprop != NULL ? SCIPpropGetName(inferprop) : "-"), inferinfo,
      oldbound, newbound);

   SCIP_CALL( varEnsureLbchginfosSize(var, blkmem, set, var->nlbchginfos+1) );
   var->lbchginfos[var->nlbchginfos].oldbound = oldbound;
   var->lbchginfos[var->nlbchginfos].newbound = newbound;
   var->lbchginfos[var->nlbchginfos].var = var;
   var->lbchginfos[var->nlbchginfos].bdchgidx.depth = depth;
   var->lbchginfos[var->nlbchginfos].bdchgidx.pos = pos;
   var->lbchginfos[var->nlbchginfos].pos = var->nlbchginfos; /*lint !e732*/
   var->lbchginfos[var->nlbchginfos].boundchgtype = boundchgtype; /*lint !e641*/
   var->lbchginfos[var->nlbchginfos].boundtype = SCIP_BOUNDTYPE_LOWER; /*lint !e641*/
   var->lbchginfos[var->nlbchginfos].redundant = FALSE;
   var->lbchginfos[var->nlbchginfos].inferboundtype = inferboundtype; /*lint !e641*/
   var->lbchginfos[var->nlbchginfos].inferencedata.var = infervar;
   var->lbchginfos[var->nlbchginfos].inferencedata.info = inferinfo;

   /**@note The "pos" data member of the bound change info has a size of 27 bits */
   assert(var->nlbchginfos < 1 << 27);

   switch( boundchgtype )
   {
   case SCIP_BOUNDCHGTYPE_BRANCHING:
      break;
   case SCIP_BOUNDCHGTYPE_CONSINFER:
      assert(infercons != NULL);
      var->lbchginfos[var->nlbchginfos].inferencedata.reason.cons = infercons;
      break;
   case SCIP_BOUNDCHGTYPE_PROPINFER:
      var->lbchginfos[var->nlbchginfos].inferencedata.reason.prop = inferprop;
      break;
   default:
      SCIPerrorMessage("invalid bound change type %d\n", boundchgtype);
      return SCIP_INVALIDDATA;
   }

   var->nlbchginfos++;

   assert(var->nlbchginfos < 2
      || SCIPbdchgidxIsEarlier(&var->lbchginfos[var->nlbchginfos-2].bdchgidx,
         &var->lbchginfos[var->nlbchginfos-1].bdchgidx));

   return SCIP_OKAY;
}

/** adds domain change info to the variable's upper bound change info array */
static
SCIP_RETCODE varAddUbchginfo(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Real             oldbound,           /**< old value for bound */
   SCIP_Real             newbound,           /**< new value for bound */
   int                   depth,              /**< depth in the tree, where the bound change takes place */
   int                   pos,                /**< position of the bound change in its bound change array */
   SCIP_VAR*             infervar,           /**< variable that was changed (parent of var, or var itself) */
   SCIP_CONS*            infercons,          /**< constraint that inferred this bound change, or NULL */
   SCIP_PROP*            inferprop,          /**< propagator that deduced the bound change, or NULL */
   int                   inferinfo,          /**< user information for inference to help resolving the conflict */
   SCIP_BOUNDTYPE        inferboundtype,     /**< type of bound for inference var: lower or upper bound */
   SCIP_BOUNDCHGTYPE     boundchgtype        /**< bound change type: branching decision or inferred bound change */
   )
{
   assert(var != NULL);
   assert(SCIPsetIsGT(set, oldbound, newbound));
   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || SCIPsetIsFeasIntegral(set, oldbound));
   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || SCIPsetIsFeasIntegral(set, newbound));
   assert(!SCIPvarIsBinary(var) || SCIPsetIsEQ(set, oldbound, 1.0));
   assert(!SCIPvarIsBinary(var) || SCIPsetIsEQ(set, newbound, 0.0));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING || infervar != NULL);
   assert((boundchgtype == SCIP_BOUNDCHGTYPE_CONSINFER) == (infercons != NULL));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_PROPINFER || inferprop == NULL);

   SCIPsetDebugMsg(set, "adding upper bound change info to var <%s>[%g,%g]: depth=%d, pos=%d, infer%s=<%s>, inferinfo=%d, %g -> %g\n",
      SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, depth, pos, infercons != NULL ? "cons" : "prop",
      infercons != NULL ? SCIPconsGetName(infercons) : (inferprop != NULL ? SCIPpropGetName(inferprop) : "-"), inferinfo,
      oldbound, newbound);

   SCIP_CALL( varEnsureUbchginfosSize(var, blkmem, set, var->nubchginfos+1) );
   var->ubchginfos[var->nubchginfos].oldbound = oldbound;
   var->ubchginfos[var->nubchginfos].newbound = newbound;
   var->ubchginfos[var->nubchginfos].var = var;
   var->ubchginfos[var->nubchginfos].bdchgidx.depth = depth;
   var->ubchginfos[var->nubchginfos].bdchgidx.pos = pos;
   var->ubchginfos[var->nubchginfos].pos = var->nubchginfos; /*lint !e732*/
   var->ubchginfos[var->nubchginfos].boundchgtype = boundchgtype; /*lint !e641*/
   var->ubchginfos[var->nubchginfos].boundtype = SCIP_BOUNDTYPE_UPPER; /*lint !e641*/
   var->ubchginfos[var->nubchginfos].redundant = FALSE;
   var->ubchginfos[var->nubchginfos].inferboundtype = inferboundtype; /*lint !e641*/
   var->ubchginfos[var->nubchginfos].inferencedata.var = infervar;
   var->ubchginfos[var->nubchginfos].inferencedata.info = inferinfo;

   /**@note The "pos" data member of the bound change info has a size of 27 bits */
   assert(var->nubchginfos < 1 << 27);

   switch( boundchgtype )
   {
   case SCIP_BOUNDCHGTYPE_BRANCHING:
      break;
   case SCIP_BOUNDCHGTYPE_CONSINFER:
      assert(infercons != NULL);
      var->ubchginfos[var->nubchginfos].inferencedata.reason.cons = infercons;
      break;
   case SCIP_BOUNDCHGTYPE_PROPINFER:
      var->ubchginfos[var->nubchginfos].inferencedata.reason.prop = inferprop;
      break;
   default:
      SCIPerrorMessage("invalid bound change type %d\n", boundchgtype);
      return SCIP_INVALIDDATA;
   }

   var->nubchginfos++;

   assert(var->nubchginfos < 2
      || SCIPbdchgidxIsEarlier(&var->ubchginfos[var->nubchginfos-2].bdchgidx,
         &var->ubchginfos[var->nubchginfos-1].bdchgidx));

   return SCIP_OKAY;
}

/** applies single bound change */
SCIP_RETCODE SCIPboundchgApply(
   SCIP_BOUNDCHG*        boundchg,           /**< bound change to apply */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   int                   depth,              /**< depth in the tree, where the bound change takes place */
   int                   pos,                /**< position of the bound change in its bound change array */
   SCIP_Bool*            cutoff              /**< pointer to store whether an infeasible bound change was detected */
   )
{
   SCIP_VAR* var;

   assert(boundchg != NULL);
   assert(stat != NULL);
   assert(depth > 0);
   assert(pos >= 0);
   assert(cutoff != NULL);

   *cutoff = FALSE;

   /* ignore redundant bound changes */
   if( boundchg->redundant )
      return SCIP_OKAY;

   var = boundchg->var;
   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
   assert(!SCIPvarIsIntegral(var) || SCIPsetIsFeasIntegral(set, boundchg->newbound));

   /* apply bound change */
   switch( boundchg->boundtype )
   {
   case SCIP_BOUNDTYPE_LOWER:
      /* check, if the bound change is still active (could be replaced by inference due to repropagation of higher node) */
      if( SCIPsetIsGT(set, boundchg->newbound, var->locdom.lb) )
      {
         if( SCIPsetIsLE(set, boundchg->newbound, var->locdom.ub) )
         {
            /* add the bound change info to the variable's bound change info array */
            switch( boundchg->boundchgtype )
            {
            case SCIP_BOUNDCHGTYPE_BRANCHING:
               SCIPsetDebugMsg(set, " -> branching: new lower bound of <%s>[%g,%g]: %g\n",
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddLbchginfo(var, blkmem, set, var->locdom.lb, boundchg->newbound, depth, pos,
                     NULL, NULL, NULL, 0, SCIP_BOUNDTYPE_LOWER, SCIP_BOUNDCHGTYPE_BRANCHING) );
               stat->lastbranchvar = var;
               stat->lastbranchdir = SCIP_BRANCHDIR_UPWARDS;
               stat->lastbranchvalue = boundchg->newbound;
               break;

            case SCIP_BOUNDCHGTYPE_CONSINFER:
               assert(boundchg->data.inferencedata.reason.cons != NULL);
               SCIPsetDebugMsg(set, " -> constraint <%s> inference: new lower bound of <%s>[%g,%g]: %g\n",
                  SCIPconsGetName(boundchg->data.inferencedata.reason.cons),
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddLbchginfo(var, blkmem, set, var->locdom.lb, boundchg->newbound, depth, pos,
                     boundchg->data.inferencedata.var, boundchg->data.inferencedata.reason.cons, NULL,
                     boundchg->data.inferencedata.info,
                     (SCIP_BOUNDTYPE)(boundchg->inferboundtype), SCIP_BOUNDCHGTYPE_CONSINFER) );
               break;

            case SCIP_BOUNDCHGTYPE_PROPINFER:
               SCIPsetDebugMsg(set, " -> propagator <%s> inference: new lower bound of <%s>[%g,%g]: %g\n",
                  boundchg->data.inferencedata.reason.prop != NULL
                  ? SCIPpropGetName(boundchg->data.inferencedata.reason.prop) : "-",
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddLbchginfo(var, blkmem, set, var->locdom.lb, boundchg->newbound, depth, pos,
                     boundchg->data.inferencedata.var, NULL, boundchg->data.inferencedata.reason.prop,
                     boundchg->data.inferencedata.info,
                     (SCIP_BOUNDTYPE)(boundchg->inferboundtype), SCIP_BOUNDCHGTYPE_PROPINFER) );
               break;

            default:
               SCIPerrorMessage("invalid bound change type %d\n", boundchg->boundchgtype);
               return SCIP_INVALIDDATA;
            }

            /* change local bound of variable */
            SCIP_CALL( SCIPvarChgLbLocal(var, blkmem, set, stat, lp, branchcand, eventqueue, boundchg->newbound) );
         }
         else
         {
            SCIPsetDebugMsg(set, " -> cutoff: new lower bound of <%s>[%g,%g]: %g\n",
               SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
            *cutoff = TRUE;
            boundchg->redundant = TRUE; /* bound change has not entered the lbchginfos array of the variable! */
         }
      }
      else
      {
         /* mark bound change to be inactive */
         SCIPsetDebugMsg(set, " -> inactive %s: new lower bound of <%s>[%g,%g]: %g\n",
            (SCIP_BOUNDCHGTYPE)boundchg->boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING ? "branching" : "inference",
            SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
         boundchg->redundant = TRUE;
      }
      break;

   case SCIP_BOUNDTYPE_UPPER:
      /* check, if the bound change is still active (could be replaced by inference due to repropagation of higher node) */
      if( SCIPsetIsLT(set, boundchg->newbound, var->locdom.ub) )
      {
         if( SCIPsetIsGE(set, boundchg->newbound, var->locdom.lb) )
         {
            /* add the bound change info to the variable's bound change info array */
            switch( boundchg->boundchgtype )
            {
            case SCIP_BOUNDCHGTYPE_BRANCHING:
               SCIPsetDebugMsg(set, " -> branching: new upper bound of <%s>[%g,%g]: %g\n",
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddUbchginfo(var, blkmem, set, var->locdom.ub, boundchg->newbound, depth, pos,
                     NULL, NULL, NULL, 0, SCIP_BOUNDTYPE_UPPER, SCIP_BOUNDCHGTYPE_BRANCHING) );
               stat->lastbranchvar = var;
               stat->lastbranchdir = SCIP_BRANCHDIR_DOWNWARDS;
               stat->lastbranchvalue = boundchg->newbound;
               break;

            case SCIP_BOUNDCHGTYPE_CONSINFER:
               assert(boundchg->data.inferencedata.reason.cons != NULL);
               SCIPsetDebugMsg(set, " -> constraint <%s> inference: new upper bound of <%s>[%g,%g]: %g\n",
                  SCIPconsGetName(boundchg->data.inferencedata.reason.cons),
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddUbchginfo(var, blkmem, set, var->locdom.ub, boundchg->newbound, depth, pos,
                     boundchg->data.inferencedata.var, boundchg->data.inferencedata.reason.cons, NULL,
                     boundchg->data.inferencedata.info,
                     (SCIP_BOUNDTYPE)(boundchg->inferboundtype), SCIP_BOUNDCHGTYPE_CONSINFER) );
               break;

            case SCIP_BOUNDCHGTYPE_PROPINFER:
               SCIPsetDebugMsg(set, " -> propagator <%s> inference: new upper bound of <%s>[%g,%g]: %g\n",
                  boundchg->data.inferencedata.reason.prop != NULL
                  ? SCIPpropGetName(boundchg->data.inferencedata.reason.prop) : "-",
                  SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
               SCIP_CALL( varAddUbchginfo(var, blkmem, set, var->locdom.ub, boundchg->newbound, depth, pos,
                     boundchg->data.inferencedata.var, NULL, boundchg->data.inferencedata.reason.prop,
                     boundchg->data.inferencedata.info,
                     (SCIP_BOUNDTYPE)(boundchg->inferboundtype), SCIP_BOUNDCHGTYPE_PROPINFER) );
               break;

            default:
               SCIPerrorMessage("invalid bound change type %d\n", boundchg->boundchgtype);
               return SCIP_INVALIDDATA;
            }

            /* change local bound of variable */
            SCIP_CALL( SCIPvarChgUbLocal(var, blkmem, set, stat, lp, branchcand, eventqueue, boundchg->newbound) );
         }
         else
         {
            SCIPsetDebugMsg(set, " -> cutoff: new upper bound of <%s>[%g,%g]: %g\n",
               SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
            *cutoff = TRUE;
            boundchg->redundant = TRUE; /* bound change has not entered the ubchginfos array of the variable! */
         }
      }
      else
      {
         /* mark bound change to be inactive */
         SCIPsetDebugMsg(set, " -> inactive %s: new upper bound of <%s>[%g,%g]: %g\n",
            (SCIP_BOUNDCHGTYPE)boundchg->boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING ? "branching" : "inference",
            SCIPvarGetName(var), var->locdom.lb, var->locdom.ub, boundchg->newbound);
         boundchg->redundant = TRUE;
      }
      break;

   default:
      SCIPerrorMessage("unknown bound type\n");
      return SCIP_INVALIDDATA;
   }

   /* update the branching and inference history */
   if( !boundchg->applied && !boundchg->redundant )
   {
      assert(var == boundchg->var);

      if( (SCIP_BOUNDCHGTYPE)boundchg->boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING )
      {
         SCIP_CALL( SCIPvarIncNBranchings(var, blkmem, set, stat,
               (SCIP_BOUNDTYPE)boundchg->boundtype == SCIP_BOUNDTYPE_LOWER
               ? SCIP_BRANCHDIR_UPWARDS : SCIP_BRANCHDIR_DOWNWARDS, boundchg->newbound, depth) );
      }
      else if( stat->lastbranchvar != NULL )
      {
         /**@todo if last branching variable is unknown, retrieve it from the nodes' boundchg arrays */
         SCIP_CALL( SCIPvarIncInferenceSum(stat->lastbranchvar, blkmem, set, stat, stat->lastbranchdir, stat->lastbranchvalue, 1.0) );
      }
      boundchg->applied = TRUE;
   }

   return SCIP_OKAY;
}

/** undoes single bound change */
SCIP_RETCODE SCIPboundchgUndo(
   SCIP_BOUNDCHG*        boundchg,           /**< bound change to remove */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue          /**< event queue */
   )
{
   SCIP_VAR* var;

   assert(boundchg != NULL);
   assert(stat != NULL);

   /* ignore redundant bound changes */
   if( boundchg->redundant )
      return SCIP_OKAY;

   var = boundchg->var;
   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);

   /* undo bound change: apply the previous bound change of variable */
   switch( boundchg->boundtype )
   {
   case SCIP_BOUNDTYPE_LOWER:
      var->nlbchginfos--;
      assert(var->nlbchginfos >= 0);
      assert(var->lbchginfos != NULL);
      assert( SCIPsetIsFeasEQ(set, var->lbchginfos[var->nlbchginfos].newbound, var->locdom.lb) ); /*lint !e777*/
      assert( SCIPsetIsFeasLE(set, boundchg->newbound, var->locdom.lb) ); /* current lb might be larger to intermediate global bound change */

      SCIPsetDebugMsg(set, "removed lower bound change info of var <%s>[%g,%g]: depth=%d, pos=%d, %g -> %g\n",
         SCIPvarGetName(var), var->locdom.lb, var->locdom.ub,
         var->lbchginfos[var->nlbchginfos].bdchgidx.depth, var->lbchginfos[var->nlbchginfos].bdchgidx.pos,
         var->lbchginfos[var->nlbchginfos].oldbound, var->lbchginfos[var->nlbchginfos].newbound);

      /* reinstall the previous local bound */
      SCIP_CALL( SCIPvarChgLbLocal(boundchg->var, blkmem, set, stat, lp, branchcand, eventqueue,
            var->lbchginfos[var->nlbchginfos].oldbound) );

      /* in case all bound changes are removed the local bound should match the global bound */
      assert(var->nlbchginfos > 0 || SCIPsetIsFeasEQ(set, var->locdom.lb, var->glbdom.lb));

      break;

   case SCIP_BOUNDTYPE_UPPER:
      var->nubchginfos--;
      assert(var->nubchginfos >= 0);
      assert(var->ubchginfos != NULL);
      assert( SCIPsetIsFeasEQ(set, var->ubchginfos[var->nubchginfos].newbound, var->locdom.ub) ); /*lint !e777*/
      assert( SCIPsetIsFeasGE(set, boundchg->newbound, var->locdom.ub) ); /* current ub might be smaller to intermediate global bound change */

      SCIPsetDebugMsg(set, "removed upper bound change info of var <%s>[%g,%g]: depth=%d, pos=%d, %g -> %g\n",
         SCIPvarGetName(var), var->locdom.lb, var->locdom.ub,
         var->ubchginfos[var->nubchginfos].bdchgidx.depth, var->ubchginfos[var->nubchginfos].bdchgidx.pos,
         var->ubchginfos[var->nubchginfos].oldbound, var->ubchginfos[var->nubchginfos].newbound);

      /* reinstall the previous local bound */
      SCIP_CALL( SCIPvarChgUbLocal(boundchg->var, blkmem, set, stat, lp, branchcand, eventqueue,
            var->ubchginfos[var->nubchginfos].oldbound) );

      /* in case all bound changes are removed the local bound should match the global bound */
      assert(var->nubchginfos > 0 || SCIPsetIsFeasEQ(set, var->locdom.ub, var->glbdom.ub));

      break;

   default:
      SCIPerrorMessage("unknown bound type\n");
      return SCIP_INVALIDDATA;
   }

   /* update last branching variable */
   if( (SCIP_BOUNDCHGTYPE)boundchg->boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING )
   {
      stat->lastbranchvar = NULL;
      stat->lastbranchvalue = SCIP_UNKNOWN;
   }

   return SCIP_OKAY;
}

/** applies single bound change to the global problem by changing the global bound of the corresponding variable */
static
SCIP_RETCODE boundchgApplyGlobal(
   SCIP_BOUNDCHG*        boundchg,           /**< bound change to apply */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_Bool*            cutoff              /**< pointer to store whether an infeasible bound change was detected */
   )
{
   SCIP_VAR* var;
   SCIP_Real newbound;
   SCIP_BOUNDTYPE boundtype;

   assert(boundchg != NULL);
   assert(cutoff != NULL);

   *cutoff = FALSE;

   /* ignore redundant bound changes */
   if( boundchg->redundant )
      return SCIP_OKAY;

   var = SCIPboundchgGetVar(boundchg);
   newbound = SCIPboundchgGetNewbound(boundchg);
   boundtype = SCIPboundchgGetBoundtype(boundchg);

   /* check if the bound change is redundant which can happen due to a (better) global bound change which was performed
    * after that bound change was applied
    *
    * @note a global bound change is not captured by the redundant member of the bound change data structure
    */
   if( (boundtype == SCIP_BOUNDTYPE_LOWER && SCIPsetIsFeasLE(set, newbound, SCIPvarGetLbGlobal(var)))
      || (boundtype == SCIP_BOUNDTYPE_UPPER && SCIPsetIsFeasGE(set, newbound, SCIPvarGetUbGlobal(var))) )
   {
      return SCIP_OKAY;
   }

   SCIPsetDebugMsg(set, "applying global bound change: <%s>[%g,%g] %s %g\n",
      SCIPvarGetName(var), SCIPvarGetLbGlobal(var), SCIPvarGetUbGlobal(var),
      boundtype == SCIP_BOUNDTYPE_LOWER ? ">=" : "<=", newbound);

   /* check for cutoff */
   if( (boundtype == SCIP_BOUNDTYPE_LOWER && SCIPsetIsFeasGT(set, newbound, SCIPvarGetUbGlobal(var)))
      || (boundtype == SCIP_BOUNDTYPE_UPPER && SCIPsetIsFeasLT(set, newbound, SCIPvarGetLbGlobal(var))) )
   {
      *cutoff = TRUE;
      return SCIP_OKAY;
   }

   /* apply bound change */
   SCIP_CALL( SCIPvarChgBdGlobal(var, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, newbound, boundtype) );

   return SCIP_OKAY;
}

/** captures branching and inference data of bound change */
static
SCIP_RETCODE boundchgCaptureData(
   SCIP_BOUNDCHG*        boundchg            /**< bound change to remove */
   )
{
   assert(boundchg != NULL);

   /* capture variable associated with the bound change */
   assert(boundchg->var != NULL);
   SCIPvarCapture(boundchg->var);

   switch( boundchg->boundchgtype )
   {
   case SCIP_BOUNDCHGTYPE_BRANCHING:
   case SCIP_BOUNDCHGTYPE_PROPINFER:
      break;

   case SCIP_BOUNDCHGTYPE_CONSINFER:
      assert(boundchg->data.inferencedata.var != NULL);
      assert(boundchg->data.inferencedata.reason.cons != NULL);
      SCIPconsCapture(boundchg->data.inferencedata.reason.cons);
      break;

   default:
      SCIPerrorMessage("invalid bound change type\n");
      return SCIP_INVALIDDATA;
   }

   return SCIP_OKAY;
}

/** releases branching and inference data of bound change */
static
SCIP_RETCODE boundchgReleaseData(
   SCIP_BOUNDCHG*        boundchg,           /**< bound change to remove */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_LP*              lp                  /**< current LP data */

   )
{
   assert(boundchg != NULL);

   switch( boundchg->boundchgtype )
   {
   case SCIP_BOUNDCHGTYPE_BRANCHING:
   case SCIP_BOUNDCHGTYPE_PROPINFER:
      break;

   case SCIP_BOUNDCHGTYPE_CONSINFER:
      assert(boundchg->data.inferencedata.var != NULL);
      assert(boundchg->data.inferencedata.reason.cons != NULL);
      SCIP_CALL( SCIPconsRelease(&boundchg->data.inferencedata.reason.cons, blkmem, set) );
      break;

   default:
      SCIPerrorMessage("invalid bound change type\n");
      return SCIP_INVALIDDATA;
   }

   /* release variable */
   assert(boundchg->var != NULL);
   SCIP_CALL( SCIPvarRelease(&boundchg->var, blkmem, set, eventqueue, lp) );

   return SCIP_OKAY;
}

/** creates empty domain change data with dynamic arrays */
static
SCIP_RETCODE domchgCreate(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change data */
   BMS_BLKMEM*           blkmem              /**< block memory */
   )
{
   assert(domchg != NULL);
   assert(blkmem != NULL);

   SCIP_ALLOC( BMSallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGDYN)) );
   (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_DYNAMIC; /*lint !e641*/
   (*domchg)->domchgdyn.nboundchgs = 0;
   (*domchg)->domchgdyn.boundchgs = NULL;
   (*domchg)->domchgdyn.nholechgs = 0;
   (*domchg)->domchgdyn.holechgs = NULL;
   (*domchg)->domchgdyn.boundchgssize = 0;
   (*domchg)->domchgdyn.holechgssize = 0;

   return SCIP_OKAY;
}

/** frees domain change data */
SCIP_RETCODE SCIPdomchgFree(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_LP*              lp                  /**< current LP data */
   )
{
   assert(domchg != NULL);
   assert(blkmem != NULL);

   if( *domchg != NULL )
   {
      int i;

      /* release variables, branching and inference data associated with the bound changes */
      for( i = 0; i < (int)(*domchg)->domchgbound.nboundchgs; ++i )
      {
         SCIP_CALL( boundchgReleaseData(&(*domchg)->domchgbound.boundchgs[i], blkmem, set, eventqueue, lp) );
      }

      /* free memory for bound and hole changes */
      switch( (*domchg)->domchgdyn.domchgtype )
      {
      case SCIP_DOMCHGTYPE_BOUND:
         BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgbound.boundchgs, (*domchg)->domchgbound.nboundchgs);
         BMSfreeBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGBOUND));
         break;
      case SCIP_DOMCHGTYPE_BOTH:
         BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgboth.boundchgs, (*domchg)->domchgboth.nboundchgs);
         BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgboth.holechgs, (*domchg)->domchgboth.nholechgs);
         BMSfreeBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGBOTH));
         break;
      case SCIP_DOMCHGTYPE_DYNAMIC:
         BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgdyn.boundchgs, (*domchg)->domchgdyn.boundchgssize);
         BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgdyn.holechgs, (*domchg)->domchgdyn.holechgssize);
         BMSfreeBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGDYN));
         break;
      default:
         SCIPerrorMessage("invalid domain change type\n");
         return SCIP_INVALIDDATA;
      }
   }

   return SCIP_OKAY;
}

/** converts a static domain change data into a dynamic one */
static
SCIP_RETCODE domchgMakeDynamic(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change data */
   BMS_BLKMEM*           blkmem              /**< block memory */
   )
{
   assert(domchg != NULL);
   assert(blkmem != NULL);

   SCIPdebugMessage("making domain change data %p pointing to %p dynamic\n", (void*)domchg, (void*)*domchg);

   if( *domchg == NULL )
   {
      SCIP_CALL( domchgCreate(domchg, blkmem) );
   }
   else
   {
      switch( (*domchg)->domchgdyn.domchgtype )
      {
      case SCIP_DOMCHGTYPE_BOUND:
         SCIP_ALLOC( BMSreallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGBOUND), sizeof(SCIP_DOMCHGDYN)) );
         (*domchg)->domchgdyn.nholechgs = 0;
         (*domchg)->domchgdyn.holechgs = NULL;
         (*domchg)->domchgdyn.boundchgssize = (int) (*domchg)->domchgdyn.nboundchgs;
         (*domchg)->domchgdyn.holechgssize = 0;
         (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_DYNAMIC; /*lint !e641*/
         break;
      case SCIP_DOMCHGTYPE_BOTH:
         SCIP_ALLOC( BMSreallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGBOTH), sizeof(SCIP_DOMCHGDYN)) );
         (*domchg)->domchgdyn.boundchgssize = (int) (*domchg)->domchgdyn.nboundchgs;
         (*domchg)->domchgdyn.holechgssize = (*domchg)->domchgdyn.nholechgs;
         (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_DYNAMIC; /*lint !e641*/
         break;
      case SCIP_DOMCHGTYPE_DYNAMIC:
         break;
      default:
         SCIPerrorMessage("invalid domain change type\n");
         return SCIP_INVALIDDATA;
      }
   }
#ifndef NDEBUG
   {
      int i;
      for( i = 0; i < (int)(*domchg)->domchgbound.nboundchgs; ++i )
         assert(SCIPvarGetType((*domchg)->domchgbound.boundchgs[i].var) == SCIP_VARTYPE_CONTINUOUS
            || EPSISINT((*domchg)->domchgbound.boundchgs[i].newbound, 1e-06));
   }
#endif

   return SCIP_OKAY;
}

/** converts a dynamic domain change data into a static one, using less memory than for a dynamic one */
SCIP_RETCODE SCIPdomchgMakeStatic(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_LP*              lp                  /**< current LP data */
   )
{
   assert(domchg != NULL);
   assert(blkmem != NULL);

   SCIPsetDebugMsg(set, "making domain change data %p pointing to %p static\n", (void*)domchg, (void*)*domchg);

   if( *domchg != NULL )
   {
      switch( (*domchg)->domchgdyn.domchgtype )
      {
      case SCIP_DOMCHGTYPE_BOUND:
         if( (*domchg)->domchgbound.nboundchgs == 0 )
         {
            SCIP_CALL( SCIPdomchgFree(domchg, blkmem, set, eventqueue, lp) );
         }
         break;
      case SCIP_DOMCHGTYPE_BOTH:
         if( (*domchg)->domchgboth.nholechgs == 0 )
         {
            if( (*domchg)->domchgbound.nboundchgs == 0 )
            {
               SCIP_CALL( SCIPdomchgFree(domchg, blkmem, set, eventqueue, lp) );
            }
            else
            {
               SCIP_ALLOC( BMSreallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGBOTH), sizeof(SCIP_DOMCHGBOUND)) );
               (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_BOUND; /*lint !e641*/
            }
         }
         break;
      case SCIP_DOMCHGTYPE_DYNAMIC:
         if( (*domchg)->domchgboth.nholechgs == 0 )
         {
            if( (*domchg)->domchgbound.nboundchgs == 0 )
            {
               SCIP_CALL( SCIPdomchgFree(domchg, blkmem, set, eventqueue, lp) );
            }
            else
            {
               /* shrink dynamic size arrays to their minimal sizes */
               SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &(*domchg)->domchgdyn.boundchgs, \
                     (*domchg)->domchgdyn.boundchgssize, (*domchg)->domchgdyn.nboundchgs) ); /*lint !e571*/
               BMSfreeBlockMemoryArrayNull(blkmem, &(*domchg)->domchgdyn.holechgs, (*domchg)->domchgdyn.holechgssize);

               /* convert into static domain change */
               SCIP_ALLOC( BMSreallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGDYN), sizeof(SCIP_DOMCHGBOUND)) );
               (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_BOUND; /*lint !e641*/
            }
         }
         else
         {
            /* shrink dynamic size arrays to their minimal sizes */
            SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &(*domchg)->domchgdyn.boundchgs, \
                  (*domchg)->domchgdyn.boundchgssize, (*domchg)->domchgdyn.nboundchgs) ); /*lint !e571*/
            SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &(*domchg)->domchgdyn.holechgs, \
                  (*domchg)->domchgdyn.holechgssize, (*domchg)->domchgdyn.nholechgs) );

            /* convert into static domain change */
            SCIP_ALLOC( BMSreallocBlockMemorySize(blkmem, domchg, sizeof(SCIP_DOMCHGDYN), sizeof(SCIP_DOMCHGBOTH)) );
            (*domchg)->domchgdyn.domchgtype = SCIP_DOMCHGTYPE_BOTH; /*lint !e641*/
         }
         break;
      default:
         SCIPerrorMessage("invalid domain change type\n");
         return SCIP_INVALIDDATA;
      }
#ifndef NDEBUG
      if( *domchg != NULL )
      {
         int i;
         for( i = 0; i < (int)(*domchg)->domchgbound.nboundchgs; ++i )
            assert(SCIPvarGetType((*domchg)->domchgbound.boundchgs[i].var) == SCIP_VARTYPE_CONTINUOUS
               || SCIPsetIsFeasIntegral(set, (*domchg)->domchgbound.boundchgs[i].newbound));
      }
#endif
   }

   return SCIP_OKAY;
}

/** ensures, that boundchgs array can store at least num entries */
static
SCIP_RETCODE domchgEnsureBoundchgsSize(
   SCIP_DOMCHG*          domchg,             /**< domain change data structure */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(domchg != NULL);
   assert(domchg->domchgdyn.domchgtype == SCIP_DOMCHGTYPE_DYNAMIC); /*lint !e641*/

   if( num > domchg->domchgdyn.boundchgssize )
   {
      int newsize;

      newsize = SCIPsetCalcMemGrowSize(set, num);
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &domchg->domchgdyn.boundchgs, domchg->domchgdyn.boundchgssize, newsize) );
      domchg->domchgdyn.boundchgssize = newsize;
   }
   assert(num <= domchg->domchgdyn.boundchgssize);

   return SCIP_OKAY;
}

/** ensures, that holechgs array can store at least num additional entries */
static
SCIP_RETCODE domchgEnsureHolechgsSize(
   SCIP_DOMCHG*          domchg,             /**< domain change data structure */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   int                   num                 /**< minimum number of additional entries to store */
   )
{
   assert(domchg != NULL);
   assert(domchg->domchgdyn.domchgtype == SCIP_DOMCHGTYPE_DYNAMIC); /*lint !e641*/

   if( num > domchg->domchgdyn.holechgssize )
   {
      int newsize;

      newsize = SCIPsetCalcMemGrowSize(set, num);
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &domchg->domchgdyn.holechgs, domchg->domchgdyn.holechgssize, newsize) );
      domchg->domchgdyn.holechgssize = newsize;
   }
   assert(num <= domchg->domchgdyn.holechgssize);

   return SCIP_OKAY;
}

/** applies domain change */
SCIP_RETCODE SCIPdomchgApply(
   SCIP_DOMCHG*          domchg,             /**< domain change to apply */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   int                   depth,              /**< depth in the tree, where the domain change takes place */
   SCIP_Bool*            cutoff              /**< pointer to store whether an infeasible domain change was detected */
   )
{
   int i;

   assert(cutoff != NULL);

   *cutoff = FALSE;

   SCIPsetDebugMsg(set, "applying domain changes at %p in depth %d\n", (void*)domchg, depth);

   if( domchg == NULL )
      return SCIP_OKAY;

   /* apply bound changes */
   for( i = 0; i < (int)domchg->domchgbound.nboundchgs; ++i )
   {
      SCIP_CALL( SCIPboundchgApply(&domchg->domchgbound.boundchgs[i], blkmem, set, stat, lp,
            branchcand, eventqueue, depth, i, cutoff) );
      if( *cutoff )
         break;
   }
   SCIPsetDebugMsg(set, " -> %u bound changes (cutoff %u)\n", domchg->domchgbound.nboundchgs, *cutoff);

   /* mark all bound changes after a cutoff redundant */
   for( ; i < (int)domchg->domchgbound.nboundchgs; ++i )
      domchg->domchgbound.boundchgs[i].redundant = TRUE;

   /* apply holelist changes */
   if( domchg->domchgdyn.domchgtype != SCIP_DOMCHGTYPE_BOUND ) /*lint !e641*/
   {
      for( i = 0; i < domchg->domchgboth.nholechgs; ++i )
         *(domchg->domchgboth.holechgs[i].ptr) = domchg->domchgboth.holechgs[i].newlist;
      SCIPsetDebugMsg(set, " -> %d hole changes\n", domchg->domchgboth.nholechgs);
   }

   return SCIP_OKAY;
}

/** undoes domain change */
SCIP_RETCODE SCIPdomchgUndo(
   SCIP_DOMCHG*          domchg,             /**< domain change to remove */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue          /**< event queue */
   )
{
   int i;

   SCIPsetDebugMsg(set, "undoing domain changes at %p\n", (void*)domchg);
   if( domchg == NULL )
      return SCIP_OKAY;

   /* undo holelist changes */
   if( domchg->domchgdyn.domchgtype != SCIP_DOMCHGTYPE_BOUND ) /*lint !e641*/
   {
      for( i = domchg->domchgboth.nholechgs-1; i >= 0; --i )
         *(domchg->domchgboth.holechgs[i].ptr) = domchg->domchgboth.holechgs[i].oldlist;
      SCIPsetDebugMsg(set, " -> %d hole changes\n", domchg->domchgboth.nholechgs);
   }

   /* undo bound changes */
   for( i = domchg->domchgbound.nboundchgs-1; i >= 0; --i )
   {
      SCIP_CALL( SCIPboundchgUndo(&domchg->domchgbound.boundchgs[i], blkmem, set, stat, lp, branchcand, eventqueue) );
   }
   SCIPsetDebugMsg(set, " -> %u bound changes\n", domchg->domchgbound.nboundchgs);

   return SCIP_OKAY;
}

/** applies domain change to the global problem */
SCIP_RETCODE SCIPdomchgApplyGlobal(
   SCIP_DOMCHG*          domchg,             /**< domain change to apply */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_Bool*            cutoff              /**< pointer to store whether an infeasible domain change was detected */
   )
{
   int i;

   assert(cutoff != NULL);

   *cutoff = FALSE;

   if( domchg == NULL )
      return SCIP_OKAY;

   SCIPsetDebugMsg(set, "applying domain changes at %p to the global problem\n", (void*)domchg);

   /* apply bound changes */
   for( i = 0; i < (int)domchg->domchgbound.nboundchgs; ++i )
   {
      SCIP_CALL( boundchgApplyGlobal(&domchg->domchgbound.boundchgs[i], blkmem, set, stat, lp,
            branchcand, eventqueue, cliquetable, cutoff) );
      if( *cutoff )
         break;
   }
   SCIPsetDebugMsg(set, " -> %u global bound changes\n", domchg->domchgbound.nboundchgs);

   /**@todo globally apply holelist changes - how can this be done without confusing pointer updates? */

   return SCIP_OKAY;
}

/** adds bound change to domain changes */
SCIP_RETCODE SCIPdomchgAddBoundchg(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change data structure */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_VAR*             var,                /**< variable to change the bounds for */
   SCIP_Real             newbound,           /**< new value for bound */
   SCIP_BOUNDTYPE        boundtype,          /**< type of bound for var: lower or upper bound */
   SCIP_BOUNDCHGTYPE     boundchgtype,       /**< type of bound change: branching decision or inference */
   SCIP_Real             lpsolval,           /**< solval of variable in last LP on path to node, or SCIP_INVALID if unknown */
   SCIP_VAR*             infervar,           /**< variable that was changed (parent of var, or var itself), or NULL */
   SCIP_CONS*            infercons,          /**< constraint that deduced the bound change, or NULL */
   SCIP_PROP*            inferprop,          /**< propagator that deduced the bound change, or NULL */
   int                   inferinfo,          /**< user information for inference to help resolving the conflict */
   SCIP_BOUNDTYPE        inferboundtype      /**< type of bound for inference var: lower or upper bound */
   )
{
   SCIP_BOUNDCHG* boundchg;

   assert(domchg != NULL);
   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
   assert(SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS || SCIPsetIsFeasIntegral(set, newbound));
   assert(!SCIPvarIsBinary(var) || SCIPsetIsEQ(set, newbound, boundtype == SCIP_BOUNDTYPE_LOWER ? 1.0 : 0.0));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING || infervar != NULL);
   assert((boundchgtype == SCIP_BOUNDCHGTYPE_CONSINFER) == (infercons != NULL));
   assert(boundchgtype == SCIP_BOUNDCHGTYPE_PROPINFER || inferprop == NULL);

   SCIPsetDebugMsg(set, "adding %s bound change <%s: %g> of variable <%s> to domain change at %p pointing to %p\n",
      boundtype == SCIP_BOUNDTYPE_LOWER ? "lower" : "upper", boundchgtype == SCIP_BOUNDCHGTYPE_BRANCHING ? "branching" : "inference",
      newbound, var->name, (void*)domchg, (void*)*domchg);

   /* if domain change data doesn't exist, create it;
    * if domain change is static, convert it into dynamic change
    */
   if( *domchg == NULL )
   {
      SCIP_CALL( domchgCreate(domchg, blkmem) );
   }
   else if( (*domchg)->domchgdyn.domchgtype != SCIP_DOMCHGTYPE_DYNAMIC ) /*lint !e641*/
   {
      SCIP_CALL( domchgMakeDynamic(domchg, blkmem) );
   }
   assert(*domchg != NULL && (*domchg)->domchgdyn.domchgtype == SCIP_DOMCHGTYPE_DYNAMIC); /*lint !e641*/

   /* get memory for additional bound change */
   SCIP_CALL( domchgEnsureBoundchgsSize(*domchg, blkmem, set, (*domchg)->domchgdyn.nboundchgs+1) );

   /* fill in the bound change data */
   boundchg = &(*domchg)->domchgdyn.boundchgs[(*domchg)->domchgdyn.nboundchgs];
   boundchg->var = var;
   switch( boundchgtype )
   {
   case SCIP_BOUNDCHGTYPE_BRANCHING:
      boundchg->data.branchingdata.lpsolval = lpsolval;
      break;
   case SCIP_BOUNDCHGTYPE_CONSINFER:
      assert(infercons != NULL);
      boundchg->data.inferencedata.var = infervar;
      boundchg->data.inferencedata.reason.cons = infercons;
      boundchg->data.inferencedata.info = inferinfo; 
      break;
   case SCIP_BOUNDCHGTYPE_PROPINFER:
      boundchg->data.inferencedata.var = infervar;
      boundchg->data.inferencedata.reason.prop = inferprop;
      boundchg->data.inferencedata.info = inferinfo; 
      break;
   default:
      SCIPerrorMessage("invalid bound change type %d\n", boundchgtype);
      return SCIP_INVALIDDATA;
   }

   boundchg->newbound = newbound;
   boundchg->boundchgtype = boundchgtype; /*lint !e641*/
   boundchg->boundtype = boundtype; /*lint !e641*/
   boundchg->inferboundtype = inferboundtype; /*lint !e641*/
   boundchg->applied = FALSE;
   boundchg->redundant = FALSE;
   (*domchg)->domchgdyn.nboundchgs++;

   /* capture branching and inference data associated with the bound changes */
   SCIP_CALL( boundchgCaptureData(boundchg) );

#ifdef SCIP_DISABLED_CODE /* expensive debug check */
#ifdef SCIP_MORE_DEBUG
   {
      int i;
      for( i = 0; i < (int)(*domchg)->domchgbound.nboundchgs; ++i )
         assert(SCIPvarGetType((*domchg)->domchgbound.boundchgs[i].var) == SCIP_VARTYPE_CONTINUOUS
            || SCIPsetIsFeasIntegral(set, (*domchg)->domchgbound.boundchgs[i].newbound));
   }
#endif
#endif

   return SCIP_OKAY;
}

/** adds hole change to domain changes */
SCIP_RETCODE SCIPdomchgAddHolechg(
   SCIP_DOMCHG**         domchg,             /**< pointer to domain change data structure */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_HOLELIST**       ptr,                /**< changed list pointer */
   SCIP_HOLELIST*        newlist,            /**< new value of list pointer */
   SCIP_HOLELIST*        oldlist             /**< old value of list pointer */
   )
{
   SCIP_HOLECHG* holechg;

   assert(domchg != NULL);
   assert(ptr != NULL);

   /* if domain change data doesn't exist, create it;
    * if domain change is static, convert it into dynamic change
    */
   if( *domchg == NULL )
   {
      SCIP_CALL( domchgCreate(domchg, blkmem) );
   }
   else if( (*domchg)->domchgdyn.domchgtype != SCIP_DOMCHGTYPE_DYNAMIC ) /*lint !e641*/
   {
      SCIP_CALL( domchgMakeDynamic(domchg, blkmem) );
   }
   assert(*domchg != NULL && (*domchg)->domchgdyn.domchgtype == SCIP_DOMCHGTYPE_DYNAMIC); /*lint !e641*/

   /* get memory for additional hole change */
   SCIP_CALL( domchgEnsureHolechgsSize(*domchg, blkmem, set, (*domchg)->domchgdyn.nholechgs+1) );

   /* fill in the hole change data */
   holechg = &(*domchg)->domchgdyn.holechgs[(*domchg)->domchgdyn.nholechgs];
   holechg->ptr = ptr;
   holechg->newlist = newlist;
   holechg->oldlist = oldlist;
   (*domchg)->domchgdyn.nholechgs++;

   return SCIP_OKAY;
}




/*
 * methods for variables 
 */

/** returns adjusted lower bound value, which is rounded for integral variable types */
static
SCIP_Real adjustedLb(
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Real             lb                  /**< lower bound to adjust */
   )
{
   if( lb < 0.0 && SCIPsetIsInfinity(set, -lb) )
      return -SCIPsetInfinity(set);
   else if( lb > 0.0 && SCIPsetIsInfinity(set, lb) )
      return SCIPsetInfinity(set);
   else if( vartype != SCIP_VARTYPE_CONTINUOUS )
      return SCIPsetFeasCeil(set, lb);
   else if( lb > 0.0 && lb < SCIPsetEpsilon(set) )
      return 0.0;
   else
      return lb;
}

/** returns adjusted upper bound value, which is rounded for integral variable types */
static
SCIP_Real adjustedUb(
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Real             ub                  /**< upper bound to adjust */
   )
{
   if( ub > 0.0 && SCIPsetIsInfinity(set, ub) )
      return SCIPsetInfinity(set);
   else if( ub < 0.0 && SCIPsetIsInfinity(set, -ub) )
      return -SCIPsetInfinity(set);
   else if( vartype != SCIP_VARTYPE_CONTINUOUS )
      return SCIPsetFeasFloor(set, ub);
   else if( ub < 0.0 && ub > -SCIPsetEpsilon(set) )
      return 0.0;
   else
      return ub;
}

/** removes (redundant) cliques, implications and variable bounds of variable from all other variables' implications and variable
 *  bounds arrays, and optionally removes them also from the variable itself
 */
SCIP_RETCODE SCIPvarRemoveCliquesImplicsVbs(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_Bool             irrelevantvar,      /**< has the variable become irrelevant? */
   SCIP_Bool             onlyredundant,      /**< should only the redundant implications and variable bounds be removed? */
   SCIP_Bool             removefromvar       /**< should the implications and variable bounds be removed from the var itself? */
   )
{
   SCIP_Real lb;
   SCIP_Real ub;

   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
   assert(SCIPvarIsActive(var) || SCIPvarGetType(var) != SCIP_VARTYPE_BINARY);

   lb = SCIPvarGetLbGlobal(var);
   ub = SCIPvarGetUbGlobal(var);

   SCIPsetDebugMsg(set, "removing %s implications and vbounds of %s<%s>[%g,%g]\n",
      onlyredundant ? "redundant" : "all", irrelevantvar ? "irrelevant " : "", SCIPvarGetName(var), lb, ub);

   /* remove implications of (fixed) binary variable */
   if( var->implics != NULL && (!onlyredundant || lb > 0.5 || ub < 0.5) )
   {
      SCIP_Bool varfixing;

      assert(SCIPvarIsBinary(var));

      varfixing = FALSE;
      do
      {
         SCIP_VAR** implvars;
         SCIP_BOUNDTYPE* impltypes;
         int nimpls;
         int i;

         nimpls = SCIPimplicsGetNImpls(var->implics, varfixing);
         implvars = SCIPimplicsGetVars(var->implics, varfixing);
         impltypes = SCIPimplicsGetTypes(var->implics, varfixing);

         for( i = 0; i < nimpls; i++ )
         {
            SCIP_VAR* implvar;
            SCIP_BOUNDTYPE impltype;

            implvar = implvars[i];
            impltype = impltypes[i];
            assert(implvar != var);

            /* remove for all implications z == 0 / 1  ==>  x <= p / x >= p (x not binary)
             * the following variable bound from x's variable bounds 
             *   x <= b*z+d (z in vubs of x)            , for z == 0 / 1  ==>  x <= p
             *   x >= b*z+d (z in vlbs of x)            , for z == 0 / 1  ==>  x >= p
             */
            if( impltype == SCIP_BOUNDTYPE_UPPER )
            {
               if( implvar->vubs != NULL ) /* implvar may have been aggregated in the mean time */
               {
                  SCIPsetDebugMsg(set, "deleting variable bound: <%s> == %u  ==>  <%s> <= %g\n",
                     SCIPvarGetName(var), varfixing, SCIPvarGetName(implvar),
                     SCIPimplicsGetBounds(var->implics, varfixing)[i]);
                  SCIP_CALL( SCIPvboundsDel(&implvar->vubs, blkmem, var, varfixing) );
                  implvar->closestvblpcount = -1;
                  var->closestvblpcount = -1;
               }
            }
            else
            {
               if( implvar->vlbs != NULL ) /* implvar may have been aggregated in the mean time */
               {
                  SCIPsetDebugMsg(set, "deleting variable bound: <%s> == %u  ==>  <%s> >= %g\n",
                     SCIPvarGetName(var), varfixing, SCIPvarGetName(implvar),
                     SCIPimplicsGetBounds(var->implics, varfixing)[i]);
                  SCIP_CALL( SCIPvboundsDel(&implvar->vlbs, blkmem, var, !varfixing) );
                  implvar->closestvblpcount = -1;
                  var->closestvblpcount = -1;
               }
            }
         }
         varfixing = !varfixing;
      }
      while( varfixing == TRUE );

      if( removefromvar )
      {
         /* free the implications data structures */
         SCIPimplicsFree(&var->implics, blkmem);
      }
   }

   /* remove the (redundant) variable lower bounds */
   if( var->vlbs != NULL )
   {
      SCIP_VAR** vars;
      SCIP_Real* coefs;
      SCIP_Real* constants;
      int nvbds;
      int newnvbds;
      int i;

      nvbds = SCIPvboundsGetNVbds(var->vlbs);
      vars = SCIPvboundsGetVars(var->vlbs);
      coefs = SCIPvboundsGetCoefs(var->vlbs);
      constants = SCIPvboundsGetConstants(var->vlbs);

      /* remove for all variable bounds x >= b*z+d the following implication from z's implications 
       *   z == ub  ==>  x >= b*ub + d           , if b > 0
       *   z == lb  ==>  x >= b*lb + d           , if b < 0
       */
      newnvbds = 0;
      for( i = 0; i < nvbds; i++ )
      {
         SCIP_VAR* implvar;
         SCIP_Real coef;

         assert(newnvbds <= i);

         implvar = vars[i];
         assert(implvar != NULL);

         coef = coefs[i];
         assert(!SCIPsetIsZero(set, coef));

         /* check, if we want to remove the variable bound */
         if( onlyredundant )
         {
            SCIP_Real vbound;

            vbound = MAX(coef * SCIPvarGetUbGlobal(implvar), coef * SCIPvarGetLbGlobal(implvar)) + constants[i];  /*lint !e666*/
            if( SCIPsetIsFeasGT(set, vbound, lb) )
            {
               /* the variable bound is not redundant: keep it */
               if( removefromvar )
               {
                  if( newnvbds < i )
                  {
                     vars[newnvbds] = implvar;
                     coefs[newnvbds] = coef;
                     constants[newnvbds] = constants[i];
                  }
                  newnvbds++;
               }
               continue;
            }
         }

         /* remove the corresponding implication */
         if( implvar->implics != NULL ) /* variable may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting implication: <%s> == %d  ==>  <%s> >= %g\n",
               SCIPvarGetName(implvar), (coef > 0.0), SCIPvarGetName(var), MAX(coef, 0.0) + constants[i]);
            SCIP_CALL( SCIPimplicsDel(&implvar->implics, blkmem, set, (coef > 0.0), var, SCIP_BOUNDTYPE_LOWER) );
         }
         if( coef > 0.0 && implvar->vubs != NULL ) /* implvar may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting variable upper bound from <%s> involving variable %s\n",
               SCIPvarGetName(implvar), SCIPvarGetName(var));
            SCIP_CALL( SCIPvboundsDel(&implvar->vubs, blkmem, var, FALSE) );
            implvar->closestvblpcount = -1;
            var->closestvblpcount = -1;
         }
         else if( coef < 0.0 && implvar->vlbs != NULL ) /* implvar may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting variable lower bound from <%s> involving variable %s\n",
               SCIPvarGetName(implvar), SCIPvarGetName(var));
            SCIP_CALL( SCIPvboundsDel(&implvar->vlbs, blkmem, var, TRUE) );
            implvar->closestvblpcount = -1;
            var->closestvblpcount = -1;
         }
      }

      if( removefromvar )
      {
         /* update the number of variable bounds */
         SCIPvboundsShrink(&var->vlbs, blkmem, newnvbds);
         var->closestvblpcount = -1;
      }
   }

   /**@todo in general, variable bounds like x >= b*z + d corresponding to an implication like z = ub ==> x >= b*ub + d 
    *       might be missing because we only add variable bounds with reasonably small value of b. thus, we currently 
    *       cannot remove such variables x from z's implications.
    */

   /* remove the (redundant) variable upper bounds */
   if( var->vubs != NULL )
   {
      SCIP_VAR** vars;
      SCIP_Real* coefs;
      SCIP_Real* constants;
      int nvbds;
      int newnvbds;
      int i;

      nvbds = SCIPvboundsGetNVbds(var->vubs);
      vars = SCIPvboundsGetVars(var->vubs);
      coefs = SCIPvboundsGetCoefs(var->vubs);
      constants = SCIPvboundsGetConstants(var->vubs);

      /* remove for all variable bounds x <= b*z+d the following implication from z's implications 
       *   z == lb  ==>  x <= b*lb + d           , if b > 0
       *   z == ub  ==>  x <= b*ub + d           , if b < 0
       */
      newnvbds = 0;
      for( i = 0; i < nvbds; i++ )
      {
         SCIP_VAR* implvar;
         SCIP_Real coef;

         assert(newnvbds <= i);

         implvar = vars[i];
         assert(implvar != NULL);

         coef = coefs[i];
         assert(!SCIPsetIsZero(set, coef));

         /* check, if we want to remove the variable bound */
         if( onlyredundant )
         {
            SCIP_Real vbound;

            vbound = MIN(coef * SCIPvarGetUbGlobal(implvar), coef * SCIPvarGetLbGlobal(implvar)) + constants[i];  /*lint !e666*/
            if( SCIPsetIsFeasLT(set, vbound, ub) )
            {
               /* the variable bound is not redundant: keep it */
               if( removefromvar )
               {
                  if( newnvbds < i )
                  {
                     vars[newnvbds] = implvar;
                     coefs[newnvbds] = coefs[i];
                     constants[newnvbds] = constants[i];
                  }
                  newnvbds++;
               }
               continue;
            }
         }

         /* remove the corresponding implication */
         if( implvar->implics != NULL ) /* variable may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting implication: <%s> == %d  ==>  <%s> <= %g\n",
               SCIPvarGetName(implvar), (coef < 0.0), SCIPvarGetName(var), MIN(coef, 0.0) + constants[i]);
            SCIP_CALL( SCIPimplicsDel(&implvar->implics, blkmem, set, (coef < 0.0), var, SCIP_BOUNDTYPE_UPPER) );
         }
         if( coef < 0.0 && implvar->vubs != NULL ) /* implvar may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting variable upper bound from <%s> involving variable %s\n",
               SCIPvarGetName(implvar), SCIPvarGetName(var));
            SCIP_CALL( SCIPvboundsDel(&implvar->vubs, blkmem, var, TRUE) );
            implvar->closestvblpcount = -1;
            var->closestvblpcount = -1;
         }
         else if( coef > 0.0 && implvar->vlbs != NULL ) /* implvar may have been aggregated in the mean time */
         {
            SCIPsetDebugMsg(set, "deleting variable lower bound from <%s> involving variable %s\n",
               SCIPvarGetName(implvar), SCIPvarGetName(var));
            SCIP_CALL( SCIPvboundsDel(&implvar->vlbs, blkmem, var, FALSE) );
            implvar->closestvblpcount = -1;
            var->closestvblpcount = -1;
         }
      }

      if( removefromvar )
      {
         /* update the number of variable bounds */
         SCIPvboundsShrink(&var->vubs, blkmem, newnvbds);
         var->closestvblpcount = -1;
      }
   }

   /* remove the variable from all cliques */
   if( SCIPvarIsBinary(var) )
      SCIPcliquelistRemoveFromCliques(var->cliquelist, cliquetable, var, irrelevantvar);

   /**@todo variable bounds like x <= b*z + d with z general integer are not removed from x's vbd arrays, because
    *       z has no link (like in the binary case) to x
    */

   return SCIP_OKAY;
}

/** sets the variable name */
static
SCIP_RETCODE varSetName(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_STAT*            stat,               /**< problem statistics, or NULL */
   const char*           name                /**< name of variable, or NULL for automatic name creation */
   )
{
   assert(blkmem != NULL);
   assert(var != NULL);

   if( name == NULL )
   {
      char s[SCIP_MAXSTRLEN];

      assert(stat != NULL);

      (void) SCIPsnprintf(s, SCIP_MAXSTRLEN, "_var%d_", stat->nvaridx);
      SCIP_ALLOC( BMSduplicateBlockMemoryArray(blkmem, &var->name, s, strlen(s)+1) );
   }
   else
   {
      SCIP_ALLOC( BMSduplicateBlockMemoryArray(blkmem, &var->name, name, strlen(name)+1) );
   }

   return SCIP_OKAY;
}


/** creates variable; if variable is of integral type, fractional bounds are automatically rounded; an integer variable
 *  with bounds zero and one is automatically converted into a binary variable
 */
static
SCIP_RETCODE varCreate(
   SCIP_VAR**            var,                /**< pointer to variable data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   const char*           name,               /**< name of variable, or NULL for automatic name creation */
   SCIP_Real             lb,                 /**< lower bound of variable */
   SCIP_Real             ub,                 /**< upper bound of variable */
   SCIP_Real             obj,                /**< objective function value */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable, or NULL */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data, or NULL */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable, or NULL */
   SCIP_VARDATA*         vardata             /**< user data for this specific variable */
   )
{
   int i;

   assert(var != NULL);
   assert(blkmem != NULL);
   assert(stat != NULL);

   /* adjust bounds of variable */
   lb = adjustedLb(set, vartype, lb);
   ub = adjustedUb(set, vartype, ub);

   /* convert [0,1]-integers into binary variables and check that binary variables have correct bounds */
   if( (SCIPsetIsEQ(set, lb, 0.0) || SCIPsetIsEQ(set, lb, 1.0))
      && (SCIPsetIsEQ(set, ub, 0.0) || SCIPsetIsEQ(set, ub, 1.0)) )
   {
      if( vartype == SCIP_VARTYPE_INTEGER )
         vartype = SCIP_VARTYPE_BINARY;
   }
   else
   {
      if( vartype == SCIP_VARTYPE_BINARY )
      {
         SCIPerrorMessage("invalid bounds [%.2g,%.2g] for binary variable <%s>\n", lb, ub, name);
         return SCIP_INVALIDDATA;
      }
   }

   assert(vartype != SCIP_VARTYPE_BINARY || SCIPsetIsEQ(set, lb, 0.0) || SCIPsetIsEQ(set, lb, 1.0));
   assert(vartype != SCIP_VARTYPE_BINARY || SCIPsetIsEQ(set, ub, 0.0) || SCIPsetIsEQ(set, ub, 1.0));

   SCIP_ALLOC( BMSallocBlockMemory(blkmem, var) );

   /* set variable's name */
   SCIP_CALL( varSetName(*var, blkmem, stat, name) );

#ifndef NDEBUG
   (*var)->scip = set->scip;
#endif
   (*var)->obj = obj;
   (*var)->unchangedobj = obj;
   (*var)->branchfactor = 1.0;
   (*var)->rootsol = 0.0;
   (*var)->bestrootsol = 0.0;
   (*var)->bestrootredcost = 0.0;
   (*var)->bestrootlpobjval = SCIP_INVALID;
   (*var)->relaxsol = 0.0;
   (*var)->nlpsol = 0.0;
   (*var)->primsolavg = 0.5 * (lb + ub);
   (*var)->conflictlb = SCIP_REAL_MIN;
   (*var)->conflictub = SCIP_REAL_MAX;
   (*var)->conflictrelaxedlb = (*var)->conflictlb;
   (*var)->conflictrelaxedub = (*var)->conflictub;
   (*var)->lazylb = -SCIPsetInfinity(set);
   (*var)->lazyub = SCIPsetInfinity(set);
   (*var)->glbdom.holelist = NULL;
   (*var)->glbdom.lb = lb;
   (*var)->glbdom.ub = ub;
   (*var)->locdom.holelist = NULL;
   (*var)->locdom.lb = lb;
   (*var)->locdom.ub = ub;
   (*var)->varcopy = varcopy;
   (*var)->vardelorig = vardelorig;
   (*var)->vartrans = vartrans;
   (*var)->vardeltrans = vardeltrans;
   (*var)->vardata = vardata;
   (*var)->parentvars = NULL;
   (*var)->negatedvar = NULL;
   (*var)->vlbs = NULL;
   (*var)->vubs = NULL;
   (*var)->implics = NULL;
   (*var)->cliquelist = NULL;
   (*var)->eventfilter = NULL;
   (*var)->lbchginfos = NULL;
   (*var)->ubchginfos = NULL;
   (*var)->index = stat->nvaridx;
   (*var)->probindex = -1;
   (*var)->pseudocandindex = -1;
   (*var)->eventqueueindexobj = -1;
   (*var)->eventqueueindexlb = -1;
   (*var)->eventqueueindexub = -1;
   (*var)->parentvarssize = 0;
   (*var)->nparentvars = 0;
   (*var)->nuses = 0;
   (*var)->branchpriority = 0;
   (*var)->branchdirection = SCIP_BRANCHDIR_AUTO; /*lint !e641*/
   (*var)->lbchginfossize = 0;
   (*var)->nlbchginfos = 0;
   (*var)->ubchginfossize = 0;
   (*var)->nubchginfos = 0;
   (*var)->conflictlbcount = 0;
   (*var)->conflictubcount = 0;
   (*var)->closestvlbidx = -1;
   (*var)->closestvubidx = -1;
   (*var)->closestvblpcount = -1;
   (*var)->initial = initial;
   (*var)->removable = removable;
   (*var)->deleted = FALSE;
   (*var)->donotaggr = FALSE;
   (*var)->donotmultaggr = FALSE;
   (*var)->vartype = vartype; /*lint !e641*/
   (*var)->pseudocostflag = FALSE;
   (*var)->eventqueueimpl = FALSE;
   (*var)->deletable = FALSE;
   (*var)->delglobalstructs = FALSE;
   (*var)->relaxationonly = FALSE;

   for( i = 0; i < NLOCKTYPES; i++ )
   {
      (*var)->nlocksdown[i] = 0;
      (*var)->nlocksup[i] = 0;
   }

   stat->nvaridx++;

   /* create branching and inference history entries */
   SCIP_CALL( SCIPhistoryCreate(&(*var)->history, blkmem) );
   SCIP_CALL( SCIPhistoryCreate(&(*var)->historycrun, blkmem) );

   /* the value based history is only created on demand */
   (*var)->valuehistory = NULL;

   return SCIP_OKAY;
}

/** creates and captures an original problem variable; an integer variable with bounds
 *  zero and one is automatically converted into a binary variable
 */
SCIP_RETCODE SCIPvarCreateOriginal(
   SCIP_VAR**            var,                /**< pointer to variable data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   const char*           name,               /**< name of variable, or NULL for automatic name creation */
   SCIP_Real             lb,                 /**< lower bound of variable */
   SCIP_Real             ub,                 /**< upper bound of variable */
   SCIP_Real             obj,                /**< objective function value */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable, or NULL */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data, or NULL */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable, or NULL */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_VARDATA*         vardata             /**< user data for this specific variable */
   )
{
   assert(var != NULL);
   assert(blkmem != NULL);
   assert(stat != NULL);

   /* create variable */
   SCIP_CALL( varCreate(var, blkmem, set, stat, name, lb, ub, obj, vartype, initial, removable,
         varcopy, vardelorig, vartrans, vardeltrans, vardata) );

   /* set variable status and data */
   (*var)->varstatus = SCIP_VARSTATUS_ORIGINAL; /*lint !e641*/
   (*var)->data.original.origdom.holelist = NULL;
   (*var)->data.original.origdom.lb = lb;
   (*var)->data.original.origdom.ub = ub;
   (*var)->data.original.transvar = NULL;

   /* capture variable */
   SCIPvarCapture(*var);

   return SCIP_OKAY;
}

/** creates and captures a loose variable belonging to the transformed problem; an integer variable with bounds
 *  zero and one is automatically converted into a binary variable
 */
SCIP_RETCODE SCIPvarCreateTransformed(
   SCIP_VAR**            var,                /**< pointer to variable data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   const char*           name,               /**< name of variable, or NULL for automatic name creation */
   SCIP_Real             lb,                 /**< lower bound of variable */
   SCIP_Real             ub,                 /**< upper bound of variable */
   SCIP_Real             obj,                /**< objective function value */
   SCIP_VARTYPE          vartype,            /**< type of variable */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable, or NULL */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data, or NULL */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable, or NULL */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_VARDATA*         vardata             /**< user data for this specific variable */
   )
{
   assert(var != NULL);
   assert(blkmem != NULL);

   /* create variable */
   SCIP_CALL( varCreate(var, blkmem, set, stat, name, lb, ub, obj, vartype, initial, removable,
         varcopy, vardelorig, vartrans, vardeltrans, vardata) );

   /* create event filter for transformed variable */
   SCIP_CALL( SCIPeventfilterCreate(&(*var)->eventfilter, blkmem) );

   /* set variable status and data */
   (*var)->varstatus = SCIP_VARSTATUS_LOOSE; /*lint !e641*/

   /* capture variable */
   SCIPvarCapture(*var);

   return SCIP_OKAY;   
}

/** copies and captures a variable from source to target SCIP; an integer variable with bounds zero and one is
 *  automatically converted into a binary variable; in case the variable data cannot be copied the variable is not
 *  copied at all
 */
SCIP_RETCODE SCIPvarCopy(
   SCIP_VAR**            var,                /**< pointer to store the target variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP*                 sourcescip,         /**< source SCIP data structure */
   SCIP_VAR*             sourcevar,          /**< source variable */
   SCIP_HASHMAP*         varmap,             /**< a hashmap to store the mapping of source variables corresponding
                                              *   target variables */
   SCIP_HASHMAP*         consmap,            /**< a hashmap to store the mapping of source constraints to the corresponding
                                              *   target constraints */
   SCIP_Bool             global              /**< should global or local bounds be used? */
   )
{
   SCIP_VARDATA* targetdata;
   SCIP_RESULT result;
   SCIP_Real lb;
   SCIP_Real ub;

   assert(set != NULL);
   assert(blkmem != NULL);
   assert(stat != NULL);
   assert(sourcescip != NULL);
   assert(sourcevar != NULL);
   assert(var != NULL);
   assert(set->stage == SCIP_STAGE_PROBLEM);
   assert(varmap != NULL);
   assert(consmap != NULL);

   /** @todo copy hole lists */
   assert(global || SCIPvarGetHolelistLocal(sourcevar) == NULL);
   assert(!global || SCIPvarGetHolelistGlobal(sourcevar) == NULL);

   result = SCIP_DIDNOTRUN;
   targetdata = NULL;

   if( SCIPvarGetStatus(sourcevar) == SCIP_VARSTATUS_ORIGINAL )
   {
      lb = SCIPvarGetLbOriginal(sourcevar);
      ub = SCIPvarGetUbOriginal(sourcevar);
   }
   else
   {
      lb = global ? SCIPvarGetLbGlobal(sourcevar) : SCIPvarGetLbLocal(sourcevar);
      ub = global ? SCIPvarGetUbGlobal(sourcevar) : SCIPvarGetUbLocal(sourcevar);
   }

   /* creates and captures the variable in the target SCIP and initialize callback methods and variable data to NULL */
   SCIP_CALL( SCIPvarCreateOriginal(var, blkmem, set, stat, SCIPvarGetName(sourcevar), 
         lb, ub, SCIPvarGetObj(sourcevar), SCIPvarGetType(sourcevar),
         SCIPvarIsInitial(sourcevar), SCIPvarIsRemovable(sourcevar), 
         NULL, NULL, NULL, NULL, NULL) );
   assert(*var != NULL);

   /* directly copy donot(mult)aggr flag */
   (*var)->donotaggr = sourcevar->donotaggr;
   (*var)->donotmultaggr = sourcevar->donotmultaggr;

   /* insert variable into mapping between source SCIP and the target SCIP */
   assert(!SCIPhashmapExists(varmap, sourcevar));
   SCIP_CALL( SCIPhashmapInsert(varmap, sourcevar, *var) );

   /* in case there exists variable data and the variable data copy callback, try to copy variable data */
   if( sourcevar->vardata != NULL && sourcevar->varcopy != NULL )
   {
      SCIP_CALL( sourcevar->varcopy(set->scip, sourcescip, sourcevar, sourcevar->vardata, 
            varmap, consmap, (*var), &targetdata, &result) );

      /* evaluate result */
      if( result != SCIP_DIDNOTRUN && result != SCIP_SUCCESS )
      {
         SCIPerrorMessage("variable data copying method returned invalid result <%d>\n", result);
         return SCIP_INVALIDRESULT;
      }

      assert(targetdata == NULL || result == SCIP_SUCCESS);

      /* if copying was successful, add the created variable data to the variable as well as all callback methods */
      if( result == SCIP_SUCCESS )
      {
         (*var)->varcopy = sourcevar->varcopy;
         (*var)->vardelorig = sourcevar->vardelorig;
         (*var)->vartrans = sourcevar->vartrans;
         (*var)->vardeltrans = sourcevar->vardeltrans;
         (*var)->vardata = targetdata;
      }
   }

   /* we initialize histories of the variables by copying the source variable-information */
   if( set->history_allowtransfer )
   {
      SCIPvarMergeHistories((*var), sourcevar, stat);
   }

   /* in case the copying was successfully, add the created variable data to the variable as well as all callback
    * methods 
    */
   if( result == SCIP_SUCCESS )
   {
      (*var)->varcopy = sourcevar->varcopy;
      (*var)->vardelorig = sourcevar->vardelorig;
      (*var)->vartrans = sourcevar->vartrans;
      (*var)->vardeltrans = sourcevar->vardeltrans;
      (*var)->vardata = targetdata;
   }

   SCIPsetDebugMsg(set, "created copy <%s> of variable <%s>\n", SCIPvarGetName(*var), SCIPvarGetName(sourcevar));

   return SCIP_OKAY;
}

/** parse given string for a SCIP_Real bound */
static
SCIP_RETCODE parseValue(
   SCIP_SET*             set,                /**< global SCIP settings */
   const char*           str,                /**< string to parse */
   SCIP_Real*            value,              /**< pointer to store the parsed value */
   char**                endptr              /**< pointer to store the final string position if successfully parsed */
   )
{
   /* first check for infinity value */
   if( strncmp(str, "+inf", 4) == 0 )
   {
      *value = SCIPsetInfinity(set);
      (*endptr) = (char*)str + 4;
   }
   else if( strncmp(str, "-inf", 4) == 0 )
   {
      *value = -SCIPsetInfinity(set);
      (*endptr) = (char*)str + 4;
   }
   else
   {
      if( !SCIPstrToRealValue(str, value, endptr) )
      {
         SCIPerrorMessage("expected value: %s.\n", str);
         return SCIP_READERROR;
      }
   }

   return SCIP_OKAY;
}

/** parse the characters as bounds */
static
SCIP_RETCODE parseBounds(
   SCIP_SET*             set,                /**< global SCIP settings */
   const char*           str,                /**< string to parse */
   char*                 type,               /**< bound type (global, local, or lazy) */
   SCIP_Real*            lb,                 /**< pointer to store the lower bound */
   SCIP_Real*            ub,                 /**< pointer to store the upper bound */
   char**                endptr              /**< pointer to store the final string position if successfully parsed (or NULL if an error occured) */
   )
{
   char token[SCIP_MAXSTRLEN];
   char* tmpend;

   SCIPsetDebugMsg(set, "parsing bounds: '%s'\n", str);

   /* get bound type */
   SCIPstrCopySection(str, ' ', ' ', type, SCIP_MAXSTRLEN, endptr);
   if ( *endptr == str
        || ( strncmp(type, "original", 8) != 0 && strncmp(type, "global", 6) != 0 && strncmp(type, "local", 5) != 0 && strncmp(type, "lazy", 4) != 0 ) )
   {
      SCIPsetDebugMsg(set, "unkown bound type\n");
      *endptr = NULL;
      return SCIP_OKAY;
   }

   SCIPsetDebugMsg(set, "parsed bound type <%s>\n", type);

   /* get lower bound */
   SCIPstrCopySection(str, '[', ',', token, SCIP_MAXSTRLEN, endptr);
   str = *endptr;
   SCIP_CALL( parseValue(set, token, lb, &tmpend) );

   /* get upper bound */
   SCIP_CALL( parseValue(set, str, ub, endptr) );

   SCIPsetDebugMsg(set, "parsed bounds: [%g,%g]\n", *lb, *ub);

   /* skip end of bounds */
   while ( **endptr != '\0' && (**endptr == ']' || **endptr == ',') )
      ++(*endptr);

   return SCIP_OKAY;
}

/** parses a given string for a variable informations */
static
SCIP_RETCODE varParse(
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   const char*           str,                /**< string to parse */
   char*                 name,               /**< pointer to store the variable name */
   SCIP_Real*            lb,                 /**< pointer to store the lower bound */
   SCIP_Real*            ub,                 /**< pointer to store the upper bound */
   SCIP_Real*            obj,                /**< pointer to store the objective coefficient */
   SCIP_VARTYPE*         vartype,            /**< pointer to store the variable type */
   SCIP_Real*            lazylb,             /**< pointer to store if the lower bound is lazy */
   SCIP_Real*            lazyub,             /**< pointer to store if the upper bound is lazy */
   SCIP_Bool             local,              /**< should the local bound be applied */
   char**                endptr,             /**< pointer to store the final string position if successfully */
   SCIP_Bool*            success             /**< pointer store if the paring process was successful */
   )
{
   SCIP_Real parsedlb;
   SCIP_Real parsedub;
   char token[SCIP_MAXSTRLEN];
   char* strptr;
   int i;

   assert(lb != NULL);
   assert(ub != NULL);
   assert(obj != NULL);
   assert(vartype != NULL);
   assert(lazylb != NULL);
   assert(lazyub != NULL);
   assert(success != NULL);

   (*success) = TRUE;

   /* copy variable type */
   SCIPstrCopySection(str, '[', ']', token, SCIP_MAXSTRLEN, endptr);
   assert(*endptr != str);
   SCIPsetDebugMsg(set, "parsed variable type <%s>\n", token);

   /* get variable type */
   if( strncmp(token, "binary", 3) == 0 )
      (*vartype) = SCIP_VARTYPE_BINARY;
   else if( strncmp(token, "integer", 3) == 0 )
      (*vartype) = SCIP_VARTYPE_INTEGER;
   else if( strncmp(token, "implicit", 3) == 0 )
      (*vartype) = SCIP_VARTYPE_IMPLINT;
   else if( strncmp(token, "continuous", 3) == 0 )
      (*vartype) = SCIP_VARTYPE_CONTINUOUS;
   else
   {
      SCIPmessagePrintWarning(messagehdlr, "unknown variable type\n");
      (*success) = FALSE;
      return SCIP_OKAY;
   }

   /* move string pointer behind variable type */
   str = *endptr;

   /* get variable name */
   SCIPstrCopySection(str, '<', '>', name, SCIP_MAXSTRLEN, endptr);
   assert(*endptr != str);
   SCIPsetDebugMsg(set, "parsed variable name <%s>\n", name);

   /* move string pointer behind variable name */
   str = *endptr;

   /* cut out objective coefficient */
   SCIPstrCopySection(str, '=', ',', token, SCIP_MAXSTRLEN, endptr);

   /* move string pointer behind objective coefficient */
   str = *endptr;

   /* get objective coefficient */
   if( !SCIPstrToRealValue(token, obj, endptr) )
   {
      *endptr = NULL;
      return SCIP_READERROR;
   }

   SCIPsetDebugMsg(set, "parsed objective coefficient <%g>\n", *obj);

   /* parse global/original bounds */
   SCIP_CALL( parseBounds(set, str, token, lb, ub, endptr) );
   if ( *endptr == NULL )
   {
      SCIPerrorMessage("Expected bound type: %s.\n", token);
      return SCIP_READERROR;
   }
   assert(strncmp(token, "global", 6) == 0 || strncmp(token, "original", 8) == 0);

   /* initialize the lazy bound */
   *lazylb = -SCIPsetInfinity(set);
   *lazyub =  SCIPsetInfinity(set);

   /* store pointer */
   strptr = *endptr;

   /* possibly parse optional local and lazy bounds */
   for( i = 0; i < 2 && *endptr != NULL && **endptr != '\0'; ++i )
   {
      /* start after previous bounds */
      strptr = *endptr;

      /* parse global bounds */
      SCIP_CALL( parseBounds(set, strptr, token, &parsedlb, &parsedub, endptr) );

      /* stop if parsing of bounds failed */
      if( *endptr == NULL )
         break;

      if( strncmp(token, "local", 5) == 0 && local )
      {
         *lb = parsedlb;
         *ub = parsedub;
      }
      else if( strncmp(token, "lazy", 4) == 0 )
      {
         *lazylb = parsedlb;
         *lazyub = parsedub;
      }
   }

   /* restore pointer */
   if ( *endptr == NULL )
      *endptr = strptr;

   /* check bounds for binary variables */
   if ( (*vartype) == SCIP_VARTYPE_BINARY )
   {
      if ( SCIPsetIsLT(set, *lb, 0.0) || SCIPsetIsGT(set, *ub, 1.0) )
      {
         SCIPerrorMessage("Parsed invalid bounds for binary variable <%s>: [%f, %f].\n", name, *lb, *ub);
         return SCIP_READERROR;
      }
      if ( !SCIPsetIsInfinity(set, -(*lazylb)) && !SCIPsetIsInfinity(set, *lazyub) && 
           ( SCIPsetIsLT(set, *lazylb, 0.0) || SCIPsetIsGT(set, *lazyub, 1.0) ) )
      {
         SCIPerrorMessage("Parsed invalid lazy bounds for binary variable <%s>: [%f, %f].\n", name, *lazylb, *lazyub);
         return SCIP_READERROR;
      }
   }

   return SCIP_OKAY;
}

/** parses variable information (in cip format) out of a string; if the parsing process was successful an original
 *  variable is created and captured; if variable is of integral type, fractional bounds are automatically rounded; an
 *  integer variable with bounds zero and one is automatically converted into a binary variable
 */
SCIP_RETCODE SCIPvarParseOriginal(
   SCIP_VAR**            var,                /**< pointer to variable data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   SCIP_STAT*            stat,               /**< problem statistics */
   const char*           str,                /**< string to parse */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable */
   SCIP_VARDATA*         vardata,            /**< user data for this specific variable */
   char**                endptr,             /**< pointer to store the final string position if successfully */
   SCIP_Bool*            success             /**< pointer store if the paring process was successful */
   )
{
   char name[SCIP_MAXSTRLEN];
   SCIP_Real lb;
   SCIP_Real ub;
   SCIP_Real obj;
   SCIP_VARTYPE vartype;
   SCIP_Real lazylb;
   SCIP_Real lazyub;

   assert(var != NULL);
   assert(blkmem != NULL);
   assert(stat != NULL);
   assert(endptr != NULL);
   assert(success != NULL);

   /* parse string in cip format for variable information */
   SCIP_CALL( varParse(set, messagehdlr, str, name, &lb, &ub, &obj, &vartype, &lazylb, &lazyub, FALSE, endptr, success) );

   if( *success ) /*lint !e774*/
   {
      /* create variable */
      SCIP_CALL( varCreate(var, blkmem, set, stat, name, lb, ub, obj, vartype, initial, removable,
            varcopy, vardelorig, vartrans, vardeltrans, vardata) );

      /* set variable status and data */
      (*var)->varstatus = SCIP_VARSTATUS_ORIGINAL; /*lint !e641*/
      (*var)->data.original.origdom.holelist = NULL;
      (*var)->data.original.origdom.lb = lb;
      (*var)->data.original.origdom.ub = ub;
      (*var)->data.original.transvar = NULL;

      /* set lazy status of variable bounds */
      (*var)->lazylb = lazylb;
      (*var)->lazyub = lazyub;

      /* capture variable */
      SCIPvarCapture(*var);
   }

   return SCIP_OKAY;
}

/** parses variable information (in cip format) out of a string; if the parsing process was successful a loose variable
 *  belonging to the transformed problem is created and captured; if variable is of integral type, fractional bounds are
 *  automatically rounded; an integer variable with bounds zero and one is automatically converted into a binary
 *  variable
 */
SCIP_RETCODE SCIPvarParseTransformed(
   SCIP_VAR**            var,                /**< pointer to variable data */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   SCIP_STAT*            stat,               /**< problem statistics */
   const char*           str,                /**< string to parse */
   SCIP_Bool             initial,            /**< should var's column be present in the initial root LP? */
   SCIP_Bool             removable,          /**< is var's column removable from the LP (due to aging or cleanup)? */
   SCIP_DECL_VARCOPY     ((*varcopy)),       /**< copies variable data if wanted to subscip, or NULL */
   SCIP_DECL_VARDELORIG  ((*vardelorig)),    /**< frees user data of original variable */
   SCIP_DECL_VARTRANS    ((*vartrans)),      /**< creates transformed user data by transforming original user data */
   SCIP_DECL_VARDELTRANS ((*vardeltrans)),   /**< frees user data of transformed variable */
   SCIP_VARDATA*         vardata,            /**< user data for this specific variable */
   char**                endptr,             /**< pointer to store the final string position if successfully */
   SCIP_Bool*            success             /**< pointer store if the paring process was successful */
   )
{
   char name[SCIP_MAXSTRLEN];
   SCIP_Real lb;
   SCIP_Real ub;
   SCIP_Real obj;
   SCIP_VARTYPE vartype;
   SCIP_Real lazylb;
   SCIP_Real lazyub;

   assert(var != NULL);
   assert(blkmem != NULL);
   assert(endptr != NULL);
   assert(success != NULL);

   /* parse string in cip format for variable information */
   SCIP_CALL( varParse(set, messagehdlr, str, name, &lb, &ub, &obj, &vartype, &lazylb, &lazyub, TRUE, endptr, success) );

   if( *success ) /*lint !e774*/
   {
      /* create variable */
      SCIP_CALL( varCreate(var, blkmem, set, stat, name, lb, ub, obj, vartype, initial, removable,
            varcopy, vardelorig, vartrans, vardeltrans, vardata) );

      /* create event filter for transformed variable */
      SCIP_CALL( SCIPeventfilterCreate(&(*var)->eventfilter, blkmem) );

      /* set variable status and data */
      (*var)->varstatus = SCIP_VARSTATUS_LOOSE; /*lint !e641*/

      /* set lazy status of variable bounds */
      (*var)->lazylb = lazylb;
      (*var)->lazyub = lazyub;

      /* capture variable */
      SCIPvarCapture(*var);
   }

   return SCIP_OKAY;   
}

/** ensures, that parentvars array of var can store at least num entries */
static
SCIP_RETCODE varEnsureParentvarsSize(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(var->nparentvars <= var->parentvarssize);

   if( num > var->parentvarssize )
   {
      int newsize;

      newsize = SCIPsetCalcMemGrowSize(set, num);
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &var->parentvars, var->parentvarssize, newsize) );
      var->parentvarssize = newsize;
   }
   assert(num <= var->parentvarssize);

   return SCIP_OKAY;
}

/** adds variable to parent list of a variable and captures parent variable */
static
SCIP_RETCODE varAddParent(
   SCIP_VAR*             var,                /**< variable to add parent to */
   BMS_BLKMEM*           blkmem,             /**< block memory of transformed problem */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_VAR*             parentvar           /**< parent variable to add */
   )
{
   assert(var != NULL);
   assert(parentvar != NULL);

   /* the direct original counterpart must be stored as first parent */
   assert(var->nparentvars == 0 || SCIPvarGetStatus(parentvar) != SCIP_VARSTATUS_ORIGINAL);

   SCIPsetDebugMsg(set, "adding parent <%s>[%p] to variable <%s>[%p] in slot %d\n",
      parentvar->name, (void*)parentvar, var->name, (void*)var, var->nparentvars);

   SCIP_CALL( varEnsureParentvarsSize(var, blkmem, set, var->nparentvars+1) );

   var->parentvars[var->nparentvars] = parentvar;
   var->nparentvars++;

   SCIPvarCapture(parentvar);

   return SCIP_OKAY;
}

/** deletes and releases all variables from the parent list of a variable, frees the memory of parents array */
static
SCIP_RETCODE varFreeParents(
   SCIP_VAR**            var,                /**< pointer to variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue (or NULL, if it's an original variable) */
   SCIP_LP*              lp                  /**< current LP data (or NULL, if it's an original variable) */
   )
{
   SCIP_VAR* parentvar;
   int i;

   SCIPsetDebugMsg(set, "free parents of <%s>\n", (*var)->name);

   /* release the parent variables and remove the link from the parent variable to the child */
   for( i = 0; i < (*var)->nparentvars; ++i )
   {
      assert((*var)->parentvars != NULL);
      parentvar = (*var)->parentvars[i];
      assert(parentvar != NULL);

      switch( SCIPvarGetStatus(parentvar) )
      {
      case SCIP_VARSTATUS_ORIGINAL:
         assert(parentvar->data.original.transvar == *var);
         assert(&parentvar->data.original.transvar != var);
         parentvar->data.original.transvar = NULL;
         break;

      case SCIP_VARSTATUS_AGGREGATED:
         assert(parentvar->data.aggregate.var == *var);
         assert(&parentvar->data.aggregate.var != var);
         parentvar->data.aggregate.var = NULL;
         break;

#if 0
      /* The following code is unclear: should the current variable be removed from its parents? */
      case SCIP_VARSTATUS_MULTAGGR:
         assert(parentvar->data.multaggr.vars != NULL);
         for( v = 0; v < parentvar->data.multaggr.nvars && parentvar->data.multaggr.vars[v] != *var; ++v )
         {}
         assert(v < parentvar->data.multaggr.nvars && parentvar->data.multaggr.vars[v] == *var);
         if( v < parentvar->data.multaggr.nvars-1 )
         {
            parentvar->data.multaggr.vars[v] = parentvar->data.multaggr.vars[parentvar->data.multaggr.nvars-1];
            parentvar->data.multaggr.scalars[v] = parentvar->data.multaggr.scalars[parentvar->data.multaggr.nvars-1];
         }
         parentvar->data.multaggr.nvars--;
         break;
#endif

      case SCIP_VARSTATUS_NEGATED:
         assert(parentvar->negatedvar == *var);
         assert((*var)->negatedvar == parentvar);
         parentvar->negatedvar = NULL;
         (*var)->negatedvar = NULL;
         break;

      default:
         SCIPerrorMessage("parent variable is neither ORIGINAL, AGGREGATED nor NEGATED\n");
         return SCIP_INVALIDDATA;
      }  /*lint !e788*/

      SCIP_CALL( SCIPvarRelease(&(*var)->parentvars[i], blkmem, set, eventqueue, lp) );
   }

   /* free parentvars array */
   BMSfreeBlockMemoryArrayNull(blkmem, &(*var)->parentvars, (*var)->parentvarssize);

   return SCIP_OKAY;
}

/** frees a variable */
static
SCIP_RETCODE varFree(
   SCIP_VAR**            var,                /**< pointer to variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue (may be NULL, if it's not a column variable) */
   SCIP_LP*              lp                  /**< current LP data (may be NULL, if it's not a column variable) */
   )
{
   assert(var != NULL);
   assert(*var != NULL);
   assert(SCIPvarGetStatus(*var) != SCIP_VARSTATUS_COLUMN || &(*var)->data.col->var != var);
   assert((*var)->nuses == 0);
   assert((*var)->probindex == -1);
   assert((*var)->nlocksup[SCIP_LOCKTYPE_MODEL] == 0);
   assert((*var)->nlocksdown[SCIP_LOCKTYPE_MODEL] == 0);

   SCIPsetDebugMsg(set, "free variable <%s> with status=%d\n", (*var)->name, SCIPvarGetStatus(*var));

   switch( SCIPvarGetStatus(*var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      assert((*var)->data.original.transvar == NULL); /* cannot free variable, if transformed variable is still existing */
      holelistFree(&(*var)->data.original.origdom.holelist, blkmem);
      assert((*var)->data.original.origdom.holelist == NULL);
      break;
   case SCIP_VARSTATUS_LOOSE:
      break;
   case SCIP_VARSTATUS_COLUMN:
      SCIP_CALL( SCIPcolFree(&(*var)->data.col, blkmem, set, eventqueue, lp) );  /* free corresponding LP column */
      break;
   case SCIP_VARSTATUS_FIXED:
   case SCIP_VARSTATUS_AGGREGATED:
      break;
   case SCIP_VARSTATUS_MULTAGGR:
      BMSfreeBlockMemoryArray(blkmem, &(*var)->data.multaggr.vars, (*var)->data.multaggr.varssize);
      BMSfreeBlockMemoryArray(blkmem, &(*var)->data.multaggr.scalars, (*var)->data.multaggr.varssize);
      break;
   case SCIP_VARSTATUS_NEGATED:
      break;
   default:
      SCIPerrorMessage("unknown variable status\n");
      return SCIP_INVALIDDATA;
   }

   /* release all parent variables and free the parentvars array */
   SCIP_CALL( varFreeParents(var, blkmem, set, eventqueue, lp) );

   /* free user data */
   if( SCIPvarGetStatus(*var) == SCIP_VARSTATUS_ORIGINAL )
   {
      if( (*var)->vardelorig != NULL )
      {
         SCIP_CALL( (*var)->vardelorig(set->scip, *var, &(*var)->vardata) );
      }
   }
   else
   {
      if( (*var)->vardeltrans != NULL )
      {
         SCIP_CALL( (*var)->vardeltrans(set->scip, *var, &(*var)->vardata) );
      }
   }

   /* free event filter */
   if( (*var)->eventfilter != NULL )
   {
      SCIP_CALL( SCIPeventfilterFree(&(*var)->eventfilter, blkmem, set) );
   }
   assert((*var)->eventfilter == NULL);

   /* free hole lists */
   holelistFree(&(*var)->glbdom.holelist, blkmem);
   holelistFree(&(*var)->locdom.holelist, blkmem);
   assert((*var)->glbdom.holelist == NULL);
   assert((*var)->locdom.holelist == NULL);

   /* free variable bounds data structures */
   SCIPvboundsFree(&(*var)->vlbs, blkmem);
   SCIPvboundsFree(&(*var)->vubs, blkmem);

   /* free implications data structures */
   SCIPimplicsFree(&(*var)->implics, blkmem);

   /* free clique list data structures */
   SCIPcliquelistFree(&(*var)->cliquelist, blkmem);

   /* free bound change information arrays */
   BMSfreeBlockMemoryArrayNull(blkmem, &(*var)->lbchginfos, (*var)->lbchginfossize);
   BMSfreeBlockMemoryArrayNull(blkmem, &(*var)->ubchginfos, (*var)->ubchginfossize);

   /* free branching and inference history entries */
   SCIPhistoryFree(&(*var)->history, blkmem);
   SCIPhistoryFree(&(*var)->historycrun, blkmem);
   SCIPvaluehistoryFree(&(*var)->valuehistory, blkmem);

   /* free variable data structure */
   BMSfreeBlockMemoryArray(blkmem, &(*var)->name, strlen((*var)->name)+1);
   BMSfreeBlockMemory(blkmem, var);

   return SCIP_OKAY;
}

/** increases usage counter of variable */
void SCIPvarCapture(
   SCIP_VAR*             var                 /**< variable */
   )
{
   assert(var != NULL);
   assert(var->nuses >= 0);

   SCIPdebugMessage("capture variable <%s> with nuses=%d\n", var->name, var->nuses);
   var->nuses++;

#ifdef DEBUGUSES_VARNAME
   if( strcmp(var->name, DEBUGUSES_VARNAME) == 0
#ifdef DEBUGUSES_PROBNAME
      && ((var->scip->transprob != NULL && strcmp(SCIPprobGetName(var->scip->transprob), DEBUGUSES_PROBNAME) == 0) ||
          strcmp(SCIPprobGetName(var->scip->origprob), DEBUGUSES_PROBNAME) == 0)
#endif
   )
   {
      printf("Captured variable " DEBUGUSES_VARNAME " in SCIP %p, now %d uses; captured at\n", (void*)var->scip, var->nuses);
      print_backtrace();
   }
#endif
}

/** decreases usage counter of variable, and frees memory if necessary */
SCIP_RETCODE SCIPvarRelease(
   SCIP_VAR**            var,                /**< pointer to variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_LP*              lp                  /**< current LP data (or NULL, if it's an original variable) */
   )
{
   assert(var != NULL);
   assert(*var != NULL);
   assert((*var)->nuses >= 1);
   assert(blkmem != NULL);
   assert((*var)->scip == set->scip);

   SCIPsetDebugMsg(set, "release variable <%s> with nuses=%d\n", (*var)->name, (*var)->nuses);
   (*var)->nuses--;

#ifdef DEBUGUSES_VARNAME
   if( strcmp((*var)->name, DEBUGUSES_VARNAME) == 0
#ifdef DEBUGUSES_PROBNAME
      && (((*var)->scip->transprob != NULL && strcmp(SCIPprobGetName((*var)->scip->transprob), DEBUGUSES_PROBNAME) == 0) ||
          strcmp(SCIPprobGetName((*var)->scip->origprob), DEBUGUSES_PROBNAME) == 0)
#endif
   )
   {
      printf("Released variable " DEBUGUSES_VARNAME " in SCIP %p, now %d uses; released at\n", (void*)(*var)->scip, (*var)->nuses);
      print_backtrace();
   }
#endif

   if( (*var)->nuses == 0 )
   {
      SCIP_CALL( varFree(var, blkmem, set, eventqueue, lp) );
   }

   *var = NULL;

   return SCIP_OKAY;
}

/** change variable name */
SCIP_RETCODE SCIPvarChgName(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   const char*           name                /**< name of variable */
   )
{
   assert(name != NULL);

   /* remove old variable name */
   BMSfreeBlockMemoryArray(blkmem, &var->name, strlen(var->name)+1);

   /* set new variable name */
   SCIP_CALL( varSetName(var, blkmem, NULL, name) );

   return SCIP_OKAY;
}

/** initializes variable data structure for solving */
void SCIPvarInitSolve(
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   assert(var != NULL);

   SCIPhistoryReset(var->historycrun);
   var->conflictlbcount = 0;
   var->conflictubcount = 0;
}

/** outputs the given bounds into the file stream */
static
void printBounds(
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   FILE*                 file,               /**< output file (or NULL for standard output) */
   SCIP_Real             lb,                 /**< lower bound */
   SCIP_Real             ub,                 /**< upper bound */
   const char*           name                /**< bound type name */
   )
{
   assert(set != NULL);

   SCIPmessageFPrintInfo(messagehdlr, file, ", %s=", name);
   if( SCIPsetIsInfinity(set, lb) )
      SCIPmessageFPrintInfo(messagehdlr, file, "[+inf,");
   else if( SCIPsetIsInfinity(set, -lb) )
      SCIPmessageFPrintInfo(messagehdlr, file, "[-inf,");
   else
      SCIPmessageFPrintInfo(messagehdlr, file, "[%.15g,", lb);
   if( SCIPsetIsInfinity(set, ub) )
      SCIPmessageFPrintInfo(messagehdlr, file, "+inf]");
   else if( SCIPsetIsInfinity(set, -ub) )
      SCIPmessageFPrintInfo(messagehdlr, file, "-inf]");
   else
      SCIPmessageFPrintInfo(messagehdlr, file, "%.15g]", ub);
}

/** prints hole list to file stream */
static
void printHolelist(
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   FILE*                 file,               /**< output file (or NULL for standard output) */
   SCIP_HOLELIST*        holelist,           /**< hole list pointer to hole of interest */
   const char*           name                /**< hole type name */
   )
{  /*lint --e{715}*/
   SCIP_Real left;
   SCIP_Real right;

   if( holelist == NULL )
      return;

   left = SCIPholelistGetLeft(holelist);
   right = SCIPholelistGetRight(holelist);

   /* display first hole */
   SCIPmessageFPrintInfo(messagehdlr, file, ", %s=(%g,%g)", name, left, right);
   holelist = SCIPholelistGetNext(holelist);

   while(holelist != NULL  )
   {
      left = SCIPholelistGetLeft(holelist);
      right = SCIPholelistGetRight(holelist);

      /* display hole */
      SCIPmessageFPrintInfo(messagehdlr, file, "(%g,%g)", left, right);

      /* get next hole */
      holelist = SCIPholelistGetNext(holelist);
   }
}

/** outputs variable information into file stream */
SCIP_RETCODE SCIPvarPrint(
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_MESSAGEHDLR*     messagehdlr,        /**< message handler */
   FILE*                 file                /**< output file (or NULL for standard output) */
   )
{
   SCIP_HOLELIST* holelist;
   SCIP_Real lb;
   SCIP_Real ub;
   int i;

   assert(var != NULL);
   assert(var->scip == set->scip);

   /* type of variable */
   switch( SCIPvarGetType(var) )
   {
   case SCIP_VARTYPE_BINARY:
      SCIPmessageFPrintInfo(messagehdlr, file, "  [binary]");
      break;
   case SCIP_VARTYPE_INTEGER:
      SCIPmessageFPrintInfo(messagehdlr, file, "  [integer]");
      break;
   case SCIP_VARTYPE_IMPLINT:
      SCIPmessageFPrintInfo(messagehdlr, file, "  [implicit]");
      break;
   case SCIP_VARTYPE_CONTINUOUS:
      SCIPmessageFPrintInfo(messagehdlr, file, "  [continuous]");
      break;
   default:
      SCIPerrorMessage("unknown variable type\n");
      SCIPABORT();
      return SCIP_ERROR; /*lint !e527*/
   }

   /* name */
   SCIPmessageFPrintInfo(messagehdlr, file, " <%s>:", var->name);

   /* objective value */
   SCIPmessageFPrintInfo(messagehdlr, file, " obj=%.15g", var->obj);

   /* bounds (global bounds for transformed variables, original bounds for original variables) */
   if( !SCIPvarIsTransformed(var) )
   {
      /* output original bound */
      lb = SCIPvarGetLbOriginal(var);
      ub = SCIPvarGetUbOriginal(var);
      printBounds(set, messagehdlr, file, lb, ub, "original bounds");

      /* output lazy bound */
      lb = SCIPvarGetLbLazy(var);
      ub = SCIPvarGetUbLazy(var);

      /* only display the lazy bounds if they are different from [-infinity,infinity] */
      if( !SCIPsetIsInfinity(set, -lb) || !SCIPsetIsInfinity(set, ub) )
         printBounds(set, messagehdlr, file, lb, ub, "lazy bounds");

      holelist = SCIPvarGetHolelistOriginal(var);
      printHolelist(messagehdlr, file, holelist, "original holes");
   }
   else
   {
      /* output global bound */
      lb = SCIPvarGetLbGlobal(var);
      ub = SCIPvarGetUbGlobal(var);
      printBounds(set, messagehdlr, file, lb, ub, "global bounds");

      /* output local bound */
      lb = SCIPvarGetLbLocal(var);
      ub = SCIPvarGetUbLocal(var);
      printBounds(set, messagehdlr, file, lb, ub, "local bounds");

      /* output lazy bound */
      lb = SCIPvarGetLbLazy(var);
      ub = SCIPvarGetUbLazy(var);

      /* only display the lazy bounds if they are different from [-infinity,infinity] */
      if( !SCIPsetIsInfinity(set, -lb) || !SCIPsetIsInfinity(set, ub) )
         printBounds(set, messagehdlr, file, lb, ub, "lazy bounds");

      /* global hole list */
      holelist = SCIPvarGetHolelistGlobal(var);
      printHolelist(messagehdlr, file, holelist, "global holes");

      /* local hole list */
      holelist = SCIPvarGetHolelistLocal(var);
      printHolelist(messagehdlr, file, holelist, "local holes");
   }

   /* fixings and aggregations */
   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
   case SCIP_VARSTATUS_LOOSE:
   case SCIP_VARSTATUS_COLUMN:
      break;

   case SCIP_VARSTATUS_FIXED:
      SCIPmessageFPrintInfo(messagehdlr, file, ", fixed:");
      if( SCIPsetIsInfinity(set, var->glbdom.lb) )
         SCIPmessageFPrintInfo(messagehdlr, file, "+inf");
      else if( SCIPsetIsInfinity(set, -var->glbdom.lb) )
         SCIPmessageFPrintInfo(messagehdlr, file, "-inf");
      else
         SCIPmessageFPrintInfo(messagehdlr, file, "%.15g", var->glbdom.lb);
      break;

   case SCIP_VARSTATUS_AGGREGATED:
      SCIPmessageFPrintInfo(messagehdlr, file, ", aggregated:");
      if( !SCIPsetIsZero(set, var->data.aggregate.constant) )
         SCIPmessageFPrintInfo(messagehdlr, file, " %.15g", var->data.aggregate.constant);
      SCIPmessageFPrintInfo(messagehdlr, file, " %+.15g<%s>", var->data.aggregate.scalar, SCIPvarGetName(var->data.aggregate.var));
      break;

   case SCIP_VARSTATUS_MULTAGGR:
      SCIPmessageFPrintInfo(messagehdlr, file, ", aggregated:");
      if( var->data.multaggr.nvars == 0 || !SCIPsetIsZero(set, var->data.multaggr.constant) )
         SCIPmessageFPrintInfo(messagehdlr, file, " %.15g", var->data.multaggr.constant);
      for( i = 0; i < var->data.multaggr.nvars; ++i )
         SCIPmessageFPrintInfo(messagehdlr, file, " %+.15g<%s>", var->data.multaggr.scalars[i], SCIPvarGetName(var->data.multaggr.vars[i]));
      break;

   case SCIP_VARSTATUS_NEGATED:
      SCIPmessageFPrintInfo(messagehdlr, file, ", negated: %.15g - <%s>", var->data.negate.constant, SCIPvarGetName(var->negatedvar));
      break;

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return SCIP_ERROR; /*lint !e527*/
   }

   SCIPmessageFPrintInfo(messagehdlr, file, "\n");

   return SCIP_OKAY;
}

/** issues a VARUNLOCKED event on the given variable */
static
SCIP_RETCODE varEventVarUnlocked(
   SCIP_VAR*             var,                /**< problem variable to change */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue          /**< event queue */
   )
{
   SCIP_EVENT* event;

   assert(var != NULL);
   assert(var->nlocksdown[SCIP_LOCKTYPE_MODEL] <= 1 && var->nlocksup[SCIP_LOCKTYPE_MODEL] <= 1);
   assert(var->scip == set->scip);

   /* issue VARUNLOCKED event on variable */
   SCIP_CALL( SCIPeventCreateVarUnlocked(&event, blkmem, var) );
   SCIP_CALL( SCIPeventqueueAdd(eventqueue, blkmem, set, NULL, NULL, NULL, NULL, &event) );

   return SCIP_OKAY;
}

/** modifies lock numbers for rounding */
SCIP_RETCODE SCIPvarAddLocks(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_LOCKTYPE         locktype,           /**< type of the variable locks */
   int                   addnlocksdown,      /**< increase in number of rounding down locks */
   int                   addnlocksup         /**< increase in number of rounding up locks */
   )
{
   SCIP_VAR* lockvar;

   assert(var != NULL);
   assert((int)locktype >= 0 && (int)locktype < (int)NLOCKTYPES); /*lint !e685 !e568 !e587 !e650*/
   assert(var->nlocksup[locktype] >= 0);
   assert(var->nlocksdown[locktype] >= 0);
   assert(var->scip == set->scip);

   if( addnlocksdown == 0 && addnlocksup == 0 )
      return SCIP_OKAY;

#ifdef SCIP_DEBUG
   SCIPsetDebugMsg(set, "add rounding locks %d/%d to variable <%s> (locks=%d/%d, type=%u)\n",
         addnlocksdown, addnlocksup, var->name, var->nlocksdown[locktype], var->nlocksup[locktype], locktype);
#endif

   lockvar = var;

   while( TRUE ) /*lint !e716 */
   {
      assert(lockvar != NULL);

      switch( SCIPvarGetStatus(lockvar) )
      {
      case SCIP_VARSTATUS_ORIGINAL:
         if( lockvar->data.original.transvar != NULL )
         {
            lockvar = lockvar->data.original.transvar;
            break;
         }
         else
         {
            lockvar->nlocksdown[locktype] += addnlocksdown;
            lockvar->nlocksup[locktype] += addnlocksup;

            assert(lockvar->nlocksdown[locktype] >= 0);
            assert(lockvar->nlocksup[locktype] >= 0);

            return SCIP_OKAY;
         }
      case SCIP_VARSTATUS_LOOSE:
      case SCIP_VARSTATUS_COLUMN:
      case SCIP_VARSTATUS_FIXED:
         lockvar->nlocksdown[locktype] += addnlocksdown;
         lockvar->nlocksup[locktype] += addnlocksup;

         assert(lockvar->nlocksdown[locktype] >= 0);
         assert(lockvar->nlocksup[locktype] >= 0);

         if( locktype == SCIP_LOCKTYPE_MODEL && lockvar->nlocksdown[locktype] <= 1
            && lockvar->nlocksup[locktype] <= 1 )
         {
            SCIP_CALL( varEventVarUnlocked(lockvar, blkmem, set, eventqueue) );
         }

         return SCIP_OKAY;
      case SCIP_VARSTATUS_AGGREGATED:
         assert(!lockvar->donotaggr);

         if( lockvar->data.aggregate.scalar < 0.0 )
         {
            int tmp = addnlocksup;

            addnlocksup = addnlocksdown;
            addnlocksdown = tmp;
         }

         lockvar = lockvar->data.aggregate.var;
         break;
      case SCIP_VARSTATUS_MULTAGGR:
      {
         int v;

         assert(!lockvar->donotmultaggr);

         lockvar->nlocksdown[locktype] += addnlocksdown;
         lockvar->nlocksup[locktype] += addnlocksup;

         assert(lockvar->nlocksdown[locktype] >= 0);
         assert(lockvar->nlocksup[locktype] >= 0);

         for( v = lockvar->data.multaggr.nvars - 1; v >= 0; --v )
         {
            if( lockvar->data.multaggr.scalars[v] > 0.0 )
            {
               SCIP_CALL( SCIPvarAddLocks(lockvar->data.multaggr.vars[v], blkmem, set, eventqueue, locktype, addnlocksdown,
                     addnlocksup) );
            }
            else
            {
               SCIP_CALL( SCIPvarAddLocks(lockvar->data.multaggr.vars[v], blkmem, set, eventqueue, locktype, addnlocksup,
                     addnlocksdown) );
            }
         }
         return SCIP_OKAY;
      }
      case SCIP_VARSTATUS_NEGATED:
      {
         int tmp = addnlocksup;

         assert(lockvar->negatedvar != NULL);
         assert(SCIPvarGetStatus(lockvar->negatedvar) != SCIP_VARSTATUS_NEGATED);
         assert(lockvar->negatedvar->negatedvar == lockvar);

         addnlocksup = addnlocksdown;
         addnlocksdown = tmp;

         lockvar = lockvar->negatedvar;
         break;
      }
      default:
         SCIPerrorMessage("unknown variable status\n");
         return SCIP_INVALIDDATA;
      }
   }
}

/** gets number of locks for rounding down of a special type */
int SCIPvarGetNLocksDownType(
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_LOCKTYPE         locktype            /**< type of variable locks */
   )
{
   int nlocks;
   int i;

   assert(var != NULL);
   assert((int)locktype >= 0 && (int)locktype < (int)NLOCKTYPES); /*lint !e685 !e568 !e587 !e650*/
   assert(var->nlocksdown[locktype] >= 0);

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar != NULL )
         return SCIPvarGetNLocksDownType(var->data.original.transvar, locktype);
      else
         return var->nlocksdown[locktype];

   case SCIP_VARSTATUS_LOOSE:
   case SCIP_VARSTATUS_COLUMN:
   case SCIP_VARSTATUS_FIXED:
      return var->nlocksdown[locktype];

   case SCIP_VARSTATUS_AGGREGATED:
      assert(!var->donotaggr);
      if( var->data.aggregate.scalar > 0.0 )
         return SCIPvarGetNLocksDownType(var->data.aggregate.var, locktype);
      else
         return SCIPvarGetNLocksUpType(var->data.aggregate.var, locktype);

   case SCIP_VARSTATUS_MULTAGGR:
      assert(!var->donotmultaggr);
      nlocks = 0;
      for( i = 0; i < var->data.multaggr.nvars; ++i )
      {
         if( var->data.multaggr.scalars[i] > 0.0 )
            nlocks += SCIPvarGetNLocksDownType(var->data.multaggr.vars[i], locktype);
         else
            nlocks += SCIPvarGetNLocksUpType(var->data.multaggr.vars[i], locktype);
      }
      return nlocks;

   case SCIP_VARSTATUS_NEGATED:
      assert(var->negatedvar != NULL);
      assert(SCIPvarGetStatus(var->negatedvar) != SCIP_VARSTATUS_NEGATED);
      assert(var->negatedvar->negatedvar == var);
      return SCIPvarGetNLocksUpType(var->negatedvar, locktype);

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return INT_MAX; /*lint !e527*/
   }
}

/** gets number of locks for rounding up of a special type */
int SCIPvarGetNLocksUpType(
   SCIP_VAR*             var,                /**< problem variable */
   SCIP_LOCKTYPE         locktype            /**< type of variable locks */
   )
{
   int nlocks;
   int i;

   assert(var != NULL);
   assert((int)locktype >= 0 && (int)locktype < (int)NLOCKTYPES); /*lint !e685 !e568 !e587 !e650*/
   assert(var->nlocksup[locktype] >= 0);

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar != NULL )
         return SCIPvarGetNLocksUpType(var->data.original.transvar, locktype);
      else
         return var->nlocksup[locktype];

   case SCIP_VARSTATUS_LOOSE:
   case SCIP_VARSTATUS_COLUMN:
   case SCIP_VARSTATUS_FIXED:
      return var->nlocksup[locktype];

   case SCIP_VARSTATUS_AGGREGATED:
      assert(!var->donotaggr);
      if( var->data.aggregate.scalar > 0.0 )
         return SCIPvarGetNLocksUpType(var->data.aggregate.var, locktype);
      else
         return SCIPvarGetNLocksDownType(var->data.aggregate.var, locktype);

   case SCIP_VARSTATUS_MULTAGGR:
      assert(!var->donotmultaggr);
      nlocks = 0;
      for( i = 0; i < var->data.multaggr.nvars; ++i )
      {
         if( var->data.multaggr.scalars[i] > 0.0 )
            nlocks += SCIPvarGetNLocksUpType(var->data.multaggr.vars[i], locktype);
         else
            nlocks += SCIPvarGetNLocksDownType(var->data.multaggr.vars[i], locktype);
      }
      return nlocks;

   case SCIP_VARSTATUS_NEGATED:
      assert(var->negatedvar != NULL);
      assert(SCIPvarGetStatus(var->negatedvar) != SCIP_VARSTATUS_NEGATED);
      assert(var->negatedvar->negatedvar == var);
      return SCIPvarGetNLocksDownType(var->negatedvar, locktype);

   default:
      SCIPerrorMessage("unknown variable status\n");
      SCIPABORT();
      return INT_MAX; /*lint !e527*/
   }
}

/** gets number of locks for rounding down
 *
 *  @note This method will always return variable locks of type model
 *
 *  @note It is recommented to use SCIPvarGetNLocksDownType()
 */
int SCIPvarGetNLocksDown(
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   return SCIPvarGetNLocksDownType(var, SCIP_LOCKTYPE_MODEL);
}

/** gets number of locks for rounding up
 *
 *  @note This method will always return variable locks of type model
 *
 *  @note It is recommented to use SCIPvarGetNLocksUpType()
 */
int SCIPvarGetNLocksUp(
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   return SCIPvarGetNLocksUpType(var, SCIP_LOCKTYPE_MODEL);
}

/** is it possible, to round variable down and stay feasible?
 *
 *  @note This method will always check w.r.t variable locks of type model
 */
SCIP_Bool SCIPvarMayRoundDown(
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   return (SCIPvarGetNLocksDownType(var, SCIP_LOCKTYPE_MODEL) == 0);
}

/** is it possible, to round variable up and stay feasible?
 *
 *  @note This method will always check w.r.t. variable locks of type model
 */
SCIP_Bool SCIPvarMayRoundUp(
   SCIP_VAR*             var                 /**< problem variable */
   )
{
   return (SCIPvarGetNLocksUpType(var, SCIP_LOCKTYPE_MODEL) == 0);
}

/** gets and captures transformed variable of a given variable; if the variable is not yet transformed,
 *  a new transformed variable for this variable is created
 */
SCIP_RETCODE SCIPvarTransform(
   SCIP_VAR*             origvar,            /**< original problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory of transformed problem */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_OBJSENSE         objsense,           /**< objective sense of original problem; transformed is always MINIMIZE */
   SCIP_VAR**            transvar            /**< pointer to store the transformed variable */
   )
{
   char name[SCIP_MAXSTRLEN];

   assert(origvar != NULL);
   assert(origvar->scip == set->scip);
   assert(SCIPvarGetStatus(origvar) == SCIP_VARSTATUS_ORIGINAL);
   assert(SCIPsetIsEQ(set, origvar->glbdom.lb, origvar->locdom.lb));
   assert(SCIPsetIsEQ(set, origvar->glbdom.ub, origvar->locdom.ub));
   assert(origvar->vlbs == NULL);
   assert(origvar->vubs == NULL);
   assert(transvar != NULL);

   /* check if variable is already transformed */
   if( origvar->data.original.transvar != NULL )
   {
      *transvar = origvar->data.original.transvar;
      SCIPvarCapture(*transvar);
   }
   else
   {
      int i;

      /* create transformed variable */
      (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "t_%s", origvar->name);
      SCIP_CALL( SCIPvarCreateTransformed(transvar, blkmem, set, stat, name,
            origvar->glbdom.lb, origvar->glbdom.ub, (SCIP_Real)objsense * origvar->obj,
            SCIPvarGetType(origvar), origvar->initial, origvar->removable,
            origvar->vardelorig, origvar->vartrans, origvar->vardeltrans, origvar->varcopy, NULL) );

      /* copy the branch factor and priority */
      (*transvar)->branchfactor = origvar->branchfactor;
      (*transvar)->branchpriority = origvar->branchpriority;
      (*transvar)->branchdirection = origvar->branchdirection; /*lint !e732*/

      /* duplicate hole lists */
      SCIP_CALL( holelistDuplicate(&(*transvar)->glbdom.holelist, blkmem, set, origvar->glbdom.holelist) );
      SCIP_CALL( holelistDuplicate(&(*transvar)->locdom.holelist, blkmem, set, origvar->locdom.holelist) );

      /* link original and transformed variable */
      origvar->data.original.transvar = *transvar;
      SCIP_CALL( varAddParent(*transvar, blkmem, set, origvar) );

      /* copy rounding locks */
      for( i = 0; i < NLOCKTYPES; i++ )
      {
         (*transvar)->nlocksdown[i] = origvar->nlocksdown[i];
         (*transvar)->nlocksup[i] = origvar->nlocksup[i];
         assert((*transvar)->nlocksdown[i] >= 0);
         assert((*transvar)->nlocksup[i] >= 0);
      }

      /* copy donot(mult)aggr status */
      (*transvar)->donotaggr = origvar->donotaggr;
      (*transvar)->donotmultaggr = origvar->donotmultaggr;

      /* copy lazy bounds */
      (*transvar)->lazylb = origvar->lazylb;
      (*transvar)->lazyub = origvar->lazyub;

      /* transfer eventual variable statistics; do not update global statistics, because this has been done
       * when original variable was created
       */
      SCIPhistoryUnite((*transvar)->history, origvar->history, FALSE);

      /* transform user data */
      if( origvar->vartrans != NULL )
      {
         SCIP_CALL( origvar->vartrans(set->scip, origvar, origvar->vardata, *transvar, &(*transvar)->vardata) );
      }
      else
         (*transvar)->vardata = origvar->vardata;
   }

   SCIPsetDebugMsg(set, "transformed variable: <%s>[%p] -> <%s>[%p]\n", origvar->name, (void*)origvar, (*transvar)->name, (void*)*transvar);

   return SCIP_OKAY;
}

/** gets corresponding transformed variable of an original or negated original variable */
SCIP_RETCODE SCIPvarGetTransformed(
   SCIP_VAR*             origvar,            /**< original problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory of transformed problem */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_VAR**            transvar            /**< pointer to store the transformed variable, or NULL if not existing yet */
   )
{
   assert(origvar != NULL);
   assert(SCIPvarGetStatus(origvar) == SCIP_VARSTATUS_ORIGINAL || SCIPvarGetStatus(origvar) == SCIP_VARSTATUS_NEGATED);
   assert(origvar->scip == set->scip);

   if( SCIPvarGetStatus(origvar) == SCIP_VARSTATUS_NEGATED )
   {
      assert(origvar->negatedvar != NULL);
      assert(SCIPvarGetStatus(origvar->negatedvar) == SCIP_VARSTATUS_ORIGINAL);

      if( origvar->negatedvar->data.original.transvar == NULL )
         *transvar = NULL;
      else
      {
         SCIP_CALL( SCIPvarNegate(origvar->negatedvar->data.original.transvar, blkmem, set, stat, transvar) );
      }
   }
   else 
      *transvar = origvar->data.original.transvar;

   return SCIP_OKAY;
}

/** converts loose transformed variable into column variable, creates LP column */
SCIP_RETCODE SCIPvarColumn(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_PROB*            prob,               /**< problem data */
   SCIP_LP*              lp                  /**< current LP data */
   )
{
   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE);
   assert(var->scip == set->scip);

   SCIPsetDebugMsg(set, "creating column for variable <%s>\n", var->name);

   /* switch variable status */
   var->varstatus = SCIP_VARSTATUS_COLUMN; /*lint !e641*/

   /* create column of variable */
   SCIP_CALL( SCIPcolCreate(&var->data.col, blkmem, set, stat, var, 0, NULL, NULL, var->removable) );

   if( var->probindex != -1 )
   {
      /* inform problem about the variable's status change */
      SCIP_CALL( SCIPprobVarChangedStatus(prob, blkmem, set, NULL, NULL, var) );

      /* inform LP, that problem variable is now a column variable and no longer loose */
      SCIP_CALL( SCIPlpUpdateVarColumn(lp, set, var) );
   }

   return SCIP_OKAY;
}

/** converts column transformed variable back into loose variable, frees LP column */
SCIP_RETCODE SCIPvarLoose(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_PROB*            prob,               /**< problem data */
   SCIP_LP*              lp                  /**< current LP data */
   )
{
   assert(var != NULL);
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN);
   assert(var->scip == set->scip);
   assert(var->data.col != NULL);
   assert(var->data.col->lppos == -1);
   assert(var->data.col->lpipos == -1);

   SCIPsetDebugMsg(set, "deleting column for variable <%s>\n", var->name);

   /* free column of variable */
   SCIP_CALL( SCIPcolFree(&var->data.col, blkmem, set, eventqueue, lp) );

   /* switch variable status */
   var->varstatus = SCIP_VARSTATUS_LOOSE; /*lint !e641*/

   if( var->probindex != -1 )
   {
      /* inform problem about the variable's status change */
      SCIP_CALL( SCIPprobVarChangedStatus(prob, blkmem, set, NULL, NULL, var) );

      /* inform LP, that problem variable is now a loose variable and no longer a column */
      SCIP_CALL( SCIPlpUpdateVarLoose(lp, set, var) );
   }

   return SCIP_OKAY;
}

/** issues a VARFIXED event on the given variable and all its parents (except ORIGINAL parents);
 *  the event issuing on the parents is necessary, because unlike with bound changes, the parent variables
 *  are not informed about a fixing of an active variable they are pointing to
 */
static
SCIP_RETCODE varEventVarFixed(
   SCIP_VAR*             var,                /**< problem variable to change */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   int                   fixeventtype        /**< is this event a fixation(0), an aggregation(1), or a
                                              *   multi-aggregation(2)
                                              */
   )
{
   SCIP_EVENT* event;
   SCIP_VARSTATUS varstatus;
   int i;

   assert(var != NULL);
   assert(var->scip == set->scip);
   assert(0 <= fixeventtype && fixeventtype <= 2);

   /* issue VARFIXED event on variable */
   SCIP_CALL( SCIPeventCreateVarFixed(&event, blkmem, var) );
   SCIP_CALL( SCIPeventqueueAdd(eventqueue, blkmem, set, NULL, NULL, NULL, NULL, &event) );

#ifndef NDEBUG
   for( i = var->nparentvars -1; i >= 0; --i )
   {
      assert(SCIPvarGetStatus(var->parentvars[i]) != SCIP_VARSTATUS_MULTAGGR);
   }
#endif

   switch( fixeventtype )
   {
   case 0:
      /* process all parents of a fixed variable */
      for( i = var->nparentvars - 1; i >= 0; --i )
      {
         varstatus = SCIPvarGetStatus(var->parentvars[i]);

         assert(varstatus != SCIP_VARSTATUS_FIXED);

         /* issue event on all not yet fixed parent variables, (that should already issued this event) except the original
          * one
          */
         if( varstatus != SCIP_VARSTATUS_ORIGINAL )
         {
            SCIP_CALL( varEventVarFixed(var->parentvars[i], blkmem, set, eventqueue, fixeventtype) );
         }
      }
      break;
   case 1:
      /* process all parents of a aggregated variable */
      for( i = var->nparentvars - 1; i >= 0; --i )
      {
         varstatus = SCIPvarGetStatus(var->parentvars[i]);

         assert(varstatus != SCIP_VARSTATUS_FIXED);

         /* issue event for not aggregated parent variable, because for these and its parents the var event was already
          * issued(, except the original one)
          *
          * @note that even before an aggregated parent variable, there might be variables, for which the vent was not
          *       yet issued
          */
         if( varstatus == SCIP_VARSTATUS_AGGREGATED )
            continue;

         if( varstatus != SCIP_VARSTATUS_ORIGINAL )
         {
            SCIP_CALL( varEventVarFixed(var->parentvars[i], blkmem, set, eventqueue, fixeventtype) );
         }
      }
      break;
   case 2:
      /* process all parents of a aggregated variable */
      for( i = var->nparentvars - 1; i >= 0; --i )
      {
         varstatus = SCIPvarGetStatus(var->parentvars[i]);

         assert(varstatus != SCIP_VARSTATUS_FIXED);

         /* issue event on all parent variables except the original one */
         if( varstatus != SCIP_VARSTATUS_ORIGINAL )
         {
            SCIP_CALL( varEventVarFixed(var->parentvars[i], blkmem, set, eventqueue, fixeventtype) );
         }
      }
      break;
   default:
      SCIPerrorMessage("unknown variable fixation event origin\n");
      return SCIP_INVALIDDATA;
   }

   return SCIP_OKAY;
}

/** converts variable into fixed variable */
SCIP_RETCODE SCIPvarFix(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_PROB*            transprob,          /**< tranformed problem data */
   SCIP_PROB*            origprob,           /**< original problem data */
   SCIP_PRIMAL*          primal,             /**< primal data */
   SCIP_TREE*            tree,               /**< branch and bound tree */
   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTFILTER*     eventfilter,        /**< event filter for global (not variable dependent) events */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_Real             fixedval,           /**< value to fix variable at */
   SCIP_Bool*            infeasible,         /**< pointer to store whether the fixing is infeasible */
   SCIP_Bool*            fixed               /**< pointer to store whether the fixing was performed (variable was unfixed) */
   )
{
   SCIP_Real obj;
   SCIP_Real childfixedval;

   assert(var != NULL);
   assert(var->scip == set->scip);
   assert(SCIPsetIsEQ(set, var->glbdom.lb, var->locdom.lb));
   assert(SCIPsetIsEQ(set, var->glbdom.ub, var->locdom.ub));
   assert(infeasible != NULL);
   assert(fixed != NULL);

   SCIPsetDebugMsg(set, "fix variable <%s>[%g,%g] to %g\n", var->name, var->glbdom.lb, var->glbdom.ub, fixedval);

   *infeasible = FALSE;
   *fixed = FALSE;

   if( SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED )
   {
      *infeasible = !SCIPsetIsFeasEQ(set, fixedval, var->locdom.lb);
      SCIPsetDebugMsg(set, " -> variable already fixed to %g (fixedval=%g): infeasible=%u\n", var->locdom.lb, fixedval, *infeasible);
      return SCIP_OKAY;
   }
   else if( (SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS && !SCIPsetIsFeasIntegral(set, fixedval))
      || SCIPsetIsFeasLT(set, fixedval, var->locdom.lb)
      || SCIPsetIsFeasGT(set, fixedval, var->locdom.ub) )
   {
      SCIPsetDebugMsg(set, " -> fixing infeasible: locdom=[%g,%g], fixedval=%g\n", var->locdom.lb, var->locdom.ub, fixedval);
      *infeasible = TRUE;
      return SCIP_OKAY;
   }

   switch( SCIPvarGetStatus(var) )
   {
   case SCIP_VARSTATUS_ORIGINAL:
      if( var->data.original.transvar == NULL )
      {
         SCIPerrorMessage("cannot fix an untransformed original variable\n");
         return SCIP_INVALIDDATA;
      }
      SCIP_CALL( SCIPvarFix(var->data.original.transvar, blkmem, set, stat, transprob, origprob, primal, tree, reopt,
            lp, branchcand, eventfilter, eventqueue, cliquetable, fixedval, infeasible, fixed) );
      break;

   case SCIP_VARSTATUS_LOOSE:
      assert(!SCIPeventqueueIsDelayed(eventqueue)); /* otherwise, the pseudo objective value update gets confused */

      /* set the fixed variable's objective value to 0.0 */
      obj = var->obj;
      SCIP_CALL( SCIPvarChgObj(var, blkmem, set, transprob, primal, lp, eventqueue, 0.0) );

      /* since we change the variable type form loose to fixed, we have to adjust the number of loose
       * variables in the LP data structure; the loose objective value (looseobjval) in the LP data structure, however,
       * gets adjusted automatically, due to the event SCIP_EVENTTYPE_OBJCHANGED which dropped in the moment where the
       * objective of this variable is set to zero
       */
      SCIPlpDecNLoosevars(lp);

      /* change variable's bounds to fixed value (thereby removing redundant implications and variable bounds) */
      holelistFree(&var->glbdom.holelist, blkmem);
      holelistFree(&var->locdom.holelist, blkmem);
      SCIP_CALL( SCIPvarChgLbGlobal(var, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, fixedval) );
      SCIP_CALL( SCIPvarChgUbGlobal(var, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, fixedval) );

      if( var->glbdom.lb != var->glbdom.ub )  /*lint !e777*/
      {
         /* explicitly set variable's bounds if the fixed value was in epsilon range of the old bound (so above call didn't set bound) */
         if( SCIPvarGetType(var) != SCIP_VARTYPE_CONTINUOUS )
         {
            /* if not continuous variable, then make sure variable is fixed to integer value */
            assert(SCIPsetIsIntegral(set, fixedval));
            fixedval = SCIPsetRound(set, fixedval);
         }
         var->glbdom.lb = fixedval;
         var->glbdom.ub = fixedval;
      }

      /* ensure local domain is fixed to same value as global domain */
      var->locdom.lb = var->glbdom.lb;
      var->locdom.ub = var->glbdom.ub;

      /* delete implications and variable bounds information */
      SCIP_CALL( SCIPvarRemoveCliquesImplicsVbs(var, blkmem, cliquetable, set, FALSE, FALSE, TRUE) );
      assert(var->vlbs == NULL);
      assert(var->vubs == NULL);
      assert(var->implics == NULL);

      /* clear the history of the variable */
      SCIPhistoryReset(var->history);
      SCIPhistoryReset(var->historycrun);

      /* convert variable into fixed variable */
      var->varstatus = SCIP_VARSTATUS_FIXED; /*lint !e641*/

      /* inform problem about the variable's status change */
      if( var->probindex != -1 )
      {
         SCIP_CALL( SCIPprobVarChangedStatus(transprob, blkmem, set, branchcand, cliquetable, var) );
      }

      /* reset the objective value of the fixed variable, thus adjusting the problem's objective offset */
      SCIP_CALL( SCIPvarAddObj(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, eventfilter, eventqueue, obj) );

      /* issue VARFIXED event */
      SCIP_CALL( varEventVarFixed(var, blkmem, set, eventqueue, 0) );

      *fixed = TRUE;
      break;

   case SCIP_VARSTATUS_COLUMN:
      SCIPerrorMessage("cannot fix a column variable\n");
      return SCIP_INVALIDDATA;

   case SCIP_VARSTATUS_FIXED:
      SCIPerrorMessage("cannot fix a fixed variable again\n");  /*lint !e527*/
      SCIPABORT(); /* case is already handled in earlier if condition */
      return SCIP_INVALIDDATA;  /*lint !e527*/

   case SCIP_VARSTATUS_AGGREGATED:
      /* fix aggregation variable y in x = a*y + c, instead of fixing x directly */
      assert(SCIPsetIsZero(set, var->obj));
      assert(!SCIPsetIsZero(set, var->data.aggregate.scalar));
      if( SCIPsetIsInfinity(set, fixedval) || SCIPsetIsInfinity(set, -fixedval) )
         childfixedval = (var->data.aggregate.scalar < 0.0 ? -fixedval : fixedval);
      else
         childfixedval = (fixedval - var->data.aggregate.constant)/var->data.aggregate.scalar;
      SCIP_CALL( SCIPvarFix(var->data.aggregate.var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp,
            branchcand, eventfilter, eventqueue, cliquetable, childfixedval, infeasible, fixed) );
      break;

   case SCIP_VARSTATUS_MULTAGGR:
      SCIPerrorMessage("cannot fix a multiple aggregated variable\n");
      SCIPABORT();
      return SCIP_INVALIDDATA;  /*lint !e527*/

   case SCIP_VARSTATUS_NEGATED:
      /* fix negation variable x in x' = offset - x, instead of fixing x' directly */
      assert(SCIPsetIsZero(set, var->obj));
      assert(var->negatedvar != NULL);
      assert(SCIPvarGetStatus(var->negatedvar) != SCIP_VARSTATUS_NEGATED);
      assert(var->negatedvar->negatedvar == var);
      SCIP_CALL( SCIPvarFix(var->negatedvar, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp,
            branchcand, eventfilter, eventqueue, cliquetable, var->data.negate.constant - fixedval, infeasible, fixed) );
      break;

   default:
      SCIPerrorMessage("unknown variable status\n");
      return SCIP_INVALIDDATA;
   }

   return SCIP_OKAY;
}

/** transforms given variables, scalars and constant to the corresponding active variables, scalars and constant
 *
 * If the number of needed active variables is greater than the available slots in the variable array, nothing happens except
 * that the required size is stored in the corresponding variable; hence, if afterwards the required size is greater than the
 * available slots (varssize), nothing happens; otherwise, the active variable representation is stored in the arrays.
 *
 * The reason for this approach is that we cannot reallocate memory, since we do not know how the
 * memory has been allocated (e.g., by a C++ 'new' or SCIP functions).
 */
SCIP_RETCODE SCIPvarGetActiveRepresentatives(
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_VAR**            vars,               /**< variable array to get active variables */
   SCIP_Real*            scalars,            /**< scalars a_1, ..., a_n in linear sum a_1*x_1 + ... + a_n*x_n + c */
   int*                  nvars,              /**< pointer to number of variables and values in vars and scalars array */
   int                   varssize,           /**< available slots in vars and scalars array */
   SCIP_Real*            constant,           /**< pointer to constant c in linear sum a_1*x_1 + ... + a_n*x_n + c  */
   int*                  requiredsize,       /**< pointer to store the required array size for the active variables */
   SCIP_Bool             mergemultiples      /**< should multiple occurrences of a var be replaced by a single coeff? */
   )
{
   SCIP_VAR** activevars;
   SCIP_Real* activescalars;
   int nactivevars;
   SCIP_Real activeconstant;
   SCIP_Bool activeconstantinf;
   int activevarssize;

   SCIP_VAR* var;
   SCIP_Real scalar;
   int v;
   int k;

   SCIP_VAR** tmpvars;
   SCIP_VAR** multvars;
   SCIP_Real* tmpscalars;
   SCIP_Real* multscalars;
   int tmpvarssize;
   int ntmpvars;
   int nmultvars;

   SCIP_VAR* multvar;
   SCIP_Real multscalar;
   SCIP_Real multconstant;
   int pos;

   int noldtmpvars;

   SCIP_VAR** tmpvars2;
   SCIP_Real* tmpscalars2;
   int tmpvarssize2;
   int ntmpvars2;

   SCIP_Bool sortagain = FALSE;

   assert(set != NULL);
   assert(nvars != NULL);
   assert(scalars != NULL || *nvars == 0);
   assert(constant != NULL);
   assert(requiredsize != NULL);
   assert(*nvars <= varssize);

   *requiredsize = 0;

   if( *nvars == 0 )
      return SCIP_OKAY;

   assert(vars != NULL);

   /* handle the "easy" case of just one variable and avoid memory allocation if the variable is already active */
   if( *nvars == 1 && (vars[0]->varstatus == ((int) SCIP_VARSTATUS_COLUMN) || vars[0]->varstatus == ((int) SCIP_VARSTATUS_LOOSE)) )
   {
      *requiredsize = 1;

      return SCIP_OKAY;
   }

   nactivevars = 0;
   activeconstant = 0.0;
   activeconstantinf = FALSE;
   activevarssize = (*nvars) * 2;
   ntmpvars = *nvars;
   tmpvarssize = *nvars;

   tmpvarssize2 = 1;

   /* allocate temporary memory */
   SCIP_CALL( SCIPsetAllocBufferArray(set, &tmpvars2, tmpvarssize2) );
   SCIP_CALL( SCIPsetAllocBufferArray(set, &tmpscalars2, tmpvarssize2) );
   SCIP_CALL( SCIPsetAllocBufferArray(set, &activevars, activevarssize) );
   SCIP_CALL( SCIPsetAllocBufferArray(set, &activescalars, activevarssize) );
   SCIP_CALL( SCIPsetDuplicateBufferArray(set, &tmpvars, vars, ntmpvars) );
   SCIP_CALL( SCIPsetDuplicateBufferArray(set, &tmpscalars, scalars, ntmpvars) );

   /* to avoid unnecessary expanding of variable arrays while disaggregating several variables multiple times combine same variables
    * first, first get all corresponding variables with status loose, column, multaggr or fixed
    */
   for( v = ntmpvars - 1; v >= 0; --v )
   {
      var = tmpvars[v];
      scalar = tmpscalars[v];

      assert(var != NULL);
      /* transforms given variable, scalar and constant to the corresponding active, fixed, or
       * multi-aggregated variable, scalar and constant; if the variable resolves to a fixed
       * variable, "scalar" will be 0.0 and the value of the sum will be stored in "constant".
       */
      SCIP_CALL( SCIPvarGetProbvarSum(&var, set, &scalar, &activeconstant) );
      assert(var != NULL);

      assert(SCIPsetIsInfinity(set, activeconstant) == (activeconstant == SCIPsetInfinity(set))); /*lint !e777*/
      assert(SCIPsetIsInfinity(set, -activeconstant) == (activeconstant == -SCIPsetInfinity(set))); /*lint !e777*/

      activeconstantinf = SCIPsetIsInfinity(set, activeconstant) || SCIPsetIsInfinity(set, -activeconstant);

      assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED);

      tmpvars[v] = var;
      tmpscalars[v] = scalar;
   }
   noldtmpvars = ntmpvars;

   /* sort all variables to combine equal variables easily */
   SCIPsortPtrReal((void**)tmpvars, tmpscalars, SCIPvarComp, noldtmpvars);
   ntmpvars = 0;
   for( v = 1; v < noldtmpvars; ++v )
   {
      /* combine same variables */
      if( SCIPvarCompare(tmpvars[v], tmpvars[ntmpvars]) == 0 )
      {
         tmpscalars[ntmpvars] += tmpscalars[v];
      }
      else
      {
         ++ntmpvars;
         if( v > ntmpvars )
         {
            tmpscalars[ntmpvars] = tmpscalars[v];
            tmpvars[ntmpvars] = tmpvars[v];
         }
      }
   }
   ++ntmpvars;

#ifdef SCIP_MORE_DEBUG
   for( v = 1; v < ntmpvars; ++v )
      assert(SCIPvarCompare(tmpvars[v], tmpvars[v-1]) > 0);
#endif

   /* collect for each variable the representation in active variables */
   while( ntmpvars >= 1 )
   {
      --ntmpvars;
      ntmpvars2 = 0;
      var = tmpvars[ntmpvars];
      scalar = tmpscalars[ntmpvars];

      assert(var != NULL);

      /* TODO: maybe we should test here on SCIPsetIsZero() instead of 0.0 */
      if( scalar == 0.0 )
         continue;

      assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR
         || SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED);

      switch( SCIPvarGetStatus(var) )
      {
      case SCIP_VARSTATUS_LOOSE:
      case SCIP_VARSTATUS_COLUMN:
         /* x = a*y + c */
         if( nactivevars >= activevarssize )
         {
            activevarssize *= 2;
            SCIP_CALL( SCIPsetReallocBufferArray(set, &activevars, activevarssize) );
            SCIP_CALL( SCIPsetReallocBufferArray(set, &activescalars, activevarssize) );
            assert(nactivevars < activevarssize);
         }
         activevars[nactivevars] = var;
         activescalars[nactivevars] = scalar;
         nactivevars++;
         break;

      case SCIP_VARSTATUS_MULTAGGR:
         /* x = a_1*y_1 + ... + a_n*y_n + c */
         nmultvars = var->data.multaggr.nvars;
         multvars = var->data.multaggr.vars;
         multscalars = var->data.multaggr.scalars;
         sortagain = TRUE;

         if( nmultvars + ntmpvars > tmpvarssize )
         {
            while( nmultvars + ntmpvars > tmpvarssize )
               tmpvarssize *= 2;
            SCIP_CALL( SCIPsetReallocBufferArray(set, &tmpvars, tmpvarssize) );
            SCIP_CALL( SCIPsetReallocBufferArray(set, &tmpscalars, tmpvarssize) );
            assert(nmultvars + ntmpvars <= tmpvarssize);
         }

         if( nmultvars > tmpvarssize2 )
         {
            while( nmultvars > tmpvarssize2 )
               tmpvarssize2 *= 2;
            SCIP_CALL( SCIPsetReallocBufferArray(set, &tmpvars2, tmpvarssize2) );
            SCIP_CALL( SCIPsetReallocBufferArray(set, &tmpscalars2, tmpvarssize2) );
            assert(nmultvars <= tmpvarssize2);
         }

         --nmultvars;

         for( ; nmultvars >= 0; --nmultvars )
         {
            multvar = multvars[nmultvars];
            multscalar = multscalars[nmultvars];
            multconstant = 0;

            assert(multvar != NULL);
            SCIP_CALL( SCIPvarGetProbvarSum(&multvar, set, &multscalar, &multconstant) );
            assert(multvar != NULL);

            assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE
               || SCIPvarGetStatus(var) == SCIP_VARSTATUS_COLUMN
               || SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR
               || SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED);

            if( !activeconstantinf )
            {
               assert(!SCIPsetIsInfinity(set, scalar) && !SCIPsetIsInfinity(set, -scalar));

               if( SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant) )
               {
                  assert(scalar != 0.0);
                  if( scalar * multconstant > 0.0 )
                  {
                     activeconstant = SCIPsetInfinity(set);
                     activeconstantinf = TRUE;
                  }
                  else
                  {
                     activeconstant = -SCIPsetInfinity(set);
                     activeconstantinf = TRUE;
                  }
               }
               else
                  activeconstant += scalar * multconstant;
            }
#ifndef NDEBUG
            else
            {
               assert(!SCIPsetIsInfinity(set, activeconstant) || !(scalar * multconstant < 0.0 &&
                     (SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant))));
               assert(!SCIPsetIsInfinity(set, -activeconstant) || !(scalar * multconstant > 0.0 &&
                     (SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant))));
            }
#endif

            if( SCIPsortedvecFindPtr((void**)tmpvars, SCIPvarComp, multvar, ntmpvars, &pos) )
            {
               assert(SCIPvarCompare(tmpvars[pos], multvar) == 0);
               tmpscalars[pos] += scalar * multscalar;
            }
            else
            {
               tmpvars2[ntmpvars2] = multvar;
               tmpscalars2[ntmpvars2] = scalar * multscalar;
               ++(ntmpvars2);
               assert(ntmpvars2 <= tmpvarssize2);
            }
         }

         if( ntmpvars2 > 0 )
         {
            /* sort all variables to combine equal variables easily */
            SCIPsortPtrReal((void**)tmpvars2, tmpscalars2, SCIPvarComp, ntmpvars2);
            pos = 0;
            for( v = 1; v < ntmpvars2; ++v )
            {
               /* combine same variables */
               if( SCIPvarCompare(tmpvars2[v], tmpvars2[pos]) == 0 )
               {
                  tmpscalars2[pos] += tmpscalars2[v];
               }
               else
               {
                  ++pos;
                  if( v > pos )
                  {
                     tmpscalars2[pos] = tmpscalars2[v];
                     tmpvars2[pos] = tmpvars2[v];
                  }
               }
            }
            ntmpvars2 = pos + 1;
#ifdef SCIP_MORE_DEBUG
            for( v = 1; v < ntmpvars2; ++v )
            {
               assert(SCIPvarCompare(tmpvars2[v], tmpvars2[v-1]) > 0);
            }
            for( v = 1; v < ntmpvars; ++v )
            {
               assert(SCIPvarCompare(tmpvars[v], tmpvars[v-1]) > 0);
            }
#endif
            v = ntmpvars - 1;
            k = ntmpvars2 - 1;
            pos = ntmpvars + ntmpvars2 - 1;
            ntmpvars += ntmpvars2;

            while( v >= 0 && k >= 0 )
            {
               assert(pos >= 0);
               assert(SCIPvarCompare(tmpvars[v], tmpvars2[k]) != 0);
               if( SCIPvarCompare(tmpvars[v], tmpvars2[k]) >= 0 )
               {
                  tmpvars[pos] = tmpvars[v];
                  tmpscalars[pos] = tmpscalars[v];
                  --v;
               }
               else
               {
                  tmpvars[pos] = tmpvars2[k];
                  tmpscalars[pos] = tmpscalars2[k];
                  --k;
               }
               --pos;
               assert(pos >= 0);
            }
            while( v >= 0 )
            {
               assert(pos >= 0);
               tmpvars[pos] = tmpvars[v];
               tmpscalars[pos] = tmpscalars[v];
               --v;
               --pos;
            }
            while( k >= 0 )
            {
               assert(pos >= 0);
               tmpvars[pos] = tmpvars2[k];
               tmpscalars[pos] = tmpscalars2[k];
               --k;
               --pos;
            }
         }
#ifdef SCIP_MORE_DEBUG
         for( v = 1; v < ntmpvars; ++v )
         {
            assert(SCIPvarCompare(tmpvars[v], tmpvars[v-1]) > 0);
         }
#endif

         if( !activeconstantinf )
         {
            assert(!SCIPsetIsInfinity(set, scalar) && !SCIPsetIsInfinity(set, -scalar));

            multconstant = SCIPvarGetMultaggrConstant(var);

            if( SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant) )
            {
               assert(scalar != 0.0);
               if( scalar * multconstant > 0.0 )
               {
                  activeconstant = SCIPsetInfinity(set);
                  activeconstantinf = TRUE;
               }
               else
               {
                  activeconstant = -SCIPsetInfinity(set);
                  activeconstantinf = TRUE;
               }
            }
            else
               activeconstant += scalar * multconstant;
         }
#ifndef NDEBUG
         else
         {
            multconstant = SCIPvarGetMultaggrConstant(var);
            assert(!SCIPsetIsInfinity(set, activeconstant) || !(scalar * multconstant < 0.0 &&
                  (SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant))));
            assert(!SCIPsetIsInfinity(set, -activeconstant) || !(scalar * multconstant > 0.0 &&
                  (SCIPsetIsInfinity(set, multconstant) || SCIPsetIsInfinity(set, -multconstant))));
         }
#endif
         break;

      case SCIP_VARSTATUS_FIXED:
      case SCIP_VARSTATUS_ORIGINAL:
      case SCIP_VARSTATUS_AGGREGATED:
      case SCIP_VARSTATUS_NEGATED:
      default:
         /* case x = c, but actually we should not be here, since SCIPvarGetProbvarSum() returns a scalar of 0.0 for
          * fixed variables and is handled already
          */
         assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_FIXED);
         assert(SCIPsetIsZero(set, var->glbdom.lb) && SCIPsetIsEQ(set, var->glbdom.lb, var->glbdom.ub));
      }
   }

   if( mergemultiples )
   {
      if( sortagain )
      {
         /* sort variable and scalar array by variable index */
         SCIPsortPtrReal((void**)activevars, activescalars, SCIPvarComp, nactivevars);

         /* eliminate duplicates and count required size */
         v = nactivevars - 1;
         while( v > 0 )
         {
            /* combine both variable since they are the same */
            if( SCIPvarCompare(activevars[v - 1], activevars[v]) == 0 )
            {
               if( activescalars[v - 1] + activescalars[v] != 0.0 )
               {
                  activescalars[v - 1] += activescalars[v];
                  --nactivevars;
                  activevars[v] = activevars[nactivevars];
                  activescalars[v] = activescalars[nactivevars];
               }
               else
               {
                  --nactivevars;
                  activevars[v] = activevars[nactivevars];
                  activescalars[v] = activescalars[nactivevars];
                  --nactivevars;
                  --v;
                  activevars[v] = activevars[nactivevars];
                  activescalars[v] = activescalars[nactivevars];
               }
            }
            --v;
         }
      }
      /* the variables were added in reverse order, we revert the order now;
       * this should not be necessary, but not doing this changes the behavior sometimes
       */
      else
      {
         SCIP_VAR* tmpvar;
         SCIP_Real tmpscalar;

         for( v = 0; v < nactivevars / 2; ++v )
         {
            tmpvar = activevars[v];
            tmpscalar = activescalars[v];
            activevars[v] = activevars[nactivevars - 1 - v];
            activescalars[v] = activescalars[nactivevars - 1 - v];
            activevars[nactivevars - 1 - v] = tmpvar;
            activescalars[nactivevars - 1 - v] = tmpscalar;
         }
      }
   }
   *requiredsize = nactivevars;

   if( varssize >= *requiredsize )
   {
      assert(vars != NULL);

      *nvars = *requiredsize;

      if( !SCIPsetIsInfinity(set, *constant) && !SCIPsetIsInfinity(set, -(*constant)) )
      {
         /* if the activeconstant is infinite, the constant pointer gets the same value, otherwise add the value */
         if( activeconstantinf )
            (*constant) = activeconstant;
         else
            (*constant) += activeconstant;
      }
#ifndef NDEBUG
      else
      {
         assert(!SCIPsetIsInfinity(set, (*constant)) || !SCIPsetIsInfinity(set, -activeconstant));
         assert(!SCIPsetIsInfinity(set, -(*constant)) || !SCIPsetIsInfinity(set, activeconstant));
      }
#endif

      /* copy active variable and scalar array to the given arrays */
      for( v = 0; v < *nvars; ++v )
      {
         vars[v] = activevars[v];
         scalars[v] = activescalars[v]; /*lint !e613*/
      }
   }

   assert(SCIPsetIsInfinity(set, *constant) == ((*constant) == SCIPsetInfinity(set))); /*lint !e777*/
   assert(SCIPsetIsInfinity(set, -(*constant)) == ((*constant) == -SCIPsetInfinity(set))); /*lint !e777*/

   SCIPsetFreeBufferArray(set, &tmpscalars);
   SCIPsetFreeBufferArray(set, &tmpvars);
   SCIPsetFreeBufferArray(set, &activescalars);
   SCIPsetFreeBufferArray(set, &activevars);
   SCIPsetFreeBufferArray(set, &tmpscalars2);
   SCIPsetFreeBufferArray(set, &tmpvars2);

   return SCIP_OKAY;
}


/** flattens aggregation graph of multi-aggregated variable in order to avoid exponential recursion later on */
SCIP_RETCODE SCIPvarFlattenAggregationGraph(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_EVENTQUEUE*      eventqueue          /**< event queue */
   )
{
   int nlocksup[NLOCKTYPES];
   int nlocksdown[NLOCKTYPES];
   SCIP_Real multconstant;
   int multvarssize;
   int nmultvars;
   int multrequiredsize;
   int i;

   assert( var != NULL );
   assert( SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR );
   assert(var->scip == set->scip);

   /* in order to update the locks on the active representation of the multi-aggregated variable, we remove all locks
    * on the current representation now and re-add the locks once the variable graph has been flattened, which
    * may lead to duplicate occurences of the same variable being merged
    *
    * Here is an example. Assume we have the multi-aggregation z = x + y.
    * z occures with positive coefficient in a <= constraint c1, so it has an uplock from there.
    * When the multi-aggregation is performed, all locks are added to the active representation,
    * so x and y both get an uplock from c1. However, z was not yet replaced by x + y in c1.
    * Next, a negation y = 1 - x is identified. Again, locks are moved, so that the uplock of y originating
    * from c1 is added to x as a downlock. Thus, x has both an up- and downlock from c1.
    * The multi-aggregation changes to z = x + 1 - x, which corresponds to the locks.
    * However, before z is replaced by that sum, SCIPvarFlattenAggregationGraph() is called
    * which changes z = x + y = x + 1 - x = 1, since it merges multiple occurences of the same variable.
    * The up- and downlock of x, however, is not removed when replacing z in c1 by its active representation,
    * because it is just 1 now. Therefore, we need to update locks when flattening the aggregation graph.
    * For this, the multi-aggregated variable knows its locks in addition to adding them to the active
    * representation, which corresponds to the locks from constraints where the variable was not replaced yet.
    * By removing the locks here, based on the old representation and adding them again after flattening,
    * we ensure that the locks are correct afterwards if coefficients were merged.
    */
   for( i = 0; i < NLOCKTYPES; ++i )
   {
      nlocksup[i] = var->nlocksup[i];
      nlocksdown[i] = var->nlocksdown[i];

      SCIP_CALL( SCIPvarAddLocks(var, blkmem, set, eventqueue, (SCIP_LOCKTYPE) i, -nlocksdown[i], -nlocksup[i]) );
   }

   multconstant = var->data.multaggr.constant;
   nmultvars = var->data.multaggr.nvars;
   multvarssize = var->data.multaggr.varssize;

   SCIP_CALL( SCIPvarGetActiveRepresentatives(set, var->data.multaggr.vars, var->data.multaggr.scalars, &nmultvars, multvarssize, &multconstant, &multrequiredsize, TRUE) );

   if( multrequiredsize > multvarssize )
   {
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &(var->data.multaggr.vars), multvarssize, multrequiredsize) );
      SCIP_ALLOC( BMSreallocBlockMemoryArray(blkmem, &(var->data.multaggr.scalars), multvarssize, multrequiredsize) );
      multvarssize = multrequiredsize;
      SCIP_CALL( SCIPvarGetActiveRepresentatives(set, var->data.multaggr.vars, var->data.multaggr.scalars, &nmultvars, multvarssize, &multconstant, &multrequiredsize, TRUE) );
      assert( multrequiredsize <= multvarssize );
   }
   /**@note After the flattening the multi aggregation might resolve to be in fact an aggregation (or even a fixing?).
    * This issue is not resolved right now, since var->data.multaggr.nvars < 2 should not cause troubles. However, one
    * may loose performance hereby, since aggregated variables are easier to handle.
    *
    * Note, that there are two cases where SCIPvarFlattenAggregationGraph() is called: The easier one is that it is
    * called while installing the multi-aggregation. in principle, the described issue could be handled straightforward
    * in this case by aggregating or fixing the variable instead.  The more complicated case is the one, when the
    * multi-aggregation is used, e.g., in linear presolving (and the variable is already declared to be multi-aggregated).
    *
    * By now, it is not allowed to fix or aggregate multi-aggregated variables which would be necessary in this case.
    *
    * The same issue appears in the SCIPvarGetProbvar...() methods.
    */

   var->data.multaggr.constant = multconstant;
   var->data.multaggr.nvars = nmultvars;
   var->data.multaggr.varssize = multvarssize;

   for( i = 0; i < NLOCKTYPES; ++i )
   {
      SCIP_CALL( SCIPvarAddLocks(var, blkmem, set, eventqueue, (SCIP_LOCKTYPE) i, nlocksdown[i], nlocksup[i]) );
   }

   return SCIP_OKAY;
}

/** merge two variable histories together; a typical use case is that \p othervar is an image of the target variable
 *  in a SCIP copy. Method should be applied with care, especially because no internal checks are performed whether
 *  the history merge is reasonable
 *
 *  @note Do not use this method if the two variables originate from two SCIP's with different objective functions, since
 *        this corrupts the variable pseudo costs
 *  @note Apply with care; no internal checks are performed if the two variables should be merged
 */
void SCIPvarMergeHistories(
   SCIP_VAR*             targetvar,          /**< the variable that should contain both histories afterwards */
   SCIP_VAR*             othervar,           /**< the variable whose history is to be merged with that of the target variable */
   SCIP_STAT*            stat                /**< problem statistics */
   )
{
   /* merge only the history of the current run into the target history */
   SCIPhistoryUnite(targetvar->history, othervar->historycrun, FALSE);

   /* apply the changes also to the global history */
   SCIPhistoryUnite(stat->glbhistory, othervar->historycrun, FALSE);
}

/** sets the history of a variable; this method is typically used within reoptimization to keep and update the variable
 *  history over several iterations
 */
void SCIPvarSetHistory(
   SCIP_VAR*             var,                /**< variable */
   SCIP_HISTORY*         history,            /**< the history which is to set */
   SCIP_STAT*            stat                /**< problem statistics */
   )
{
   /* merge only the history of the current run into the target history */
   SCIPhistoryUnite(var->history, history, FALSE);

   /* apply the changes also to the global history */
   SCIPhistoryUnite(stat->glbhistory, history, FALSE);
}

/** tightens the bounds of both variables in aggregation x = a*y + c */
static
SCIP_RETCODE varUpdateAggregationBounds(
   SCIP_VAR*             var,                /**< problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_PROB*            transprob,          /**< tranformed problem data */
   SCIP_PROB*            origprob,           /**< original problem data */
   SCIP_PRIMAL*          primal,             /**< primal data */
   SCIP_TREE*            tree,               /**< branch and bound tree */
   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTFILTER*     eventfilter,        /**< event filter for global (not variable dependent) events */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_VAR*             aggvar,             /**< variable y in aggregation x = a*y + c */
   SCIP_Real             scalar,             /**< multiplier a in aggregation x = a*y + c */
   SCIP_Real             constant,           /**< constant shift c in aggregation x = a*y + c */
   SCIP_Bool*            infeasible,         /**< pointer to store whether the aggregation is infeasible */
   SCIP_Bool*            fixed               /**< pointer to store whether the variables were fixed */
   )
{
   SCIP_Real varlb;
   SCIP_Real varub;
   SCIP_Real aggvarlb;
   SCIP_Real aggvarub;
   SCIP_Bool aggvarbdschanged;

   assert(var != NULL);
   assert(var->scip == set->scip);
   assert(aggvar != NULL);
   assert(!SCIPsetIsZero(set, scalar));
   assert(infeasible != NULL);
   assert(fixed != NULL);

   *infeasible = FALSE;
   *fixed = FALSE;

   SCIPsetDebugMsg(set, "updating bounds of variables in aggregation <%s> == %g*<%s> %+g\n", var->name, scalar, aggvar->name, constant);
   SCIPsetDebugMsg(set, "  old bounds: <%s> [%g,%g]   <%s> [%g,%g]\n",
      var->name, var->glbdom.lb, var->glbdom.ub, aggvar->name, aggvar->glbdom.lb, aggvar->glbdom.ub);

   /* loop as long additional changes may be found */
   do
   {
      aggvarbdschanged = FALSE;

      /* update the bounds of the aggregated variable x in x = a*y + c */
      if( scalar > 0.0 )
      {
         if( SCIPsetIsInfinity(set, -aggvar->glbdom.lb) )
            varlb = -SCIPsetInfinity(set);
         else
            varlb = aggvar->glbdom.lb * scalar + constant;
         if( SCIPsetIsInfinity(set, aggvar->glbdom.ub) )
            varub = SCIPsetInfinity(set);
         else
            varub = aggvar->glbdom.ub * scalar + constant;
      }
      else
      {
         if( SCIPsetIsInfinity(set, -aggvar->glbdom.lb) )
            varub = SCIPsetInfinity(set);
         else
            varub = aggvar->glbdom.lb * scalar + constant;
         if( SCIPsetIsInfinity(set, aggvar->glbdom.ub) )
            varlb = -SCIPsetInfinity(set);
         else
            varlb = aggvar->glbdom.ub * scalar + constant;
      }
      varlb = MAX(varlb, var->glbdom.lb);
      varub = MIN(varub, var->glbdom.ub);
      SCIPvarAdjustLb(var, set, &varlb);
      SCIPvarAdjustUb(var, set, &varub);

      /* check the new bounds */
      if( SCIPsetIsGT(set, varlb, varub) )
      {
         /* the aggregation is infeasible */
         *infeasible = TRUE;
         return SCIP_OKAY;
      }
      else if( SCIPsetIsEQ(set, varlb, varub) )
      {
         /* the aggregated variable is fixed -> fix both variables */
         SCIP_CALL( SCIPvarFix(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand,
               eventfilter, eventqueue, cliquetable, varlb, infeasible, fixed) );
         if( !(*infeasible) )
         {
            SCIP_Bool aggfixed;

            SCIP_CALL( SCIPvarFix(aggvar, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand,
                  eventfilter, eventqueue, cliquetable, (varlb-constant)/scalar, infeasible, &aggfixed) );
            assert(*fixed == aggfixed);
         }
         return SCIP_OKAY;
      }
      else
      {
         if( SCIPsetIsGT(set, varlb, var->glbdom.lb) )
         {
            SCIP_CALL( SCIPvarChgLbGlobal(var, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, varlb) );
         }
         if( SCIPsetIsLT(set, varub, var->glbdom.ub) )
         {
            SCIP_CALL( SCIPvarChgUbGlobal(var, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, varub) );
         }

         /* update the hole list of the aggregation variable */
         /**@todo update hole list of aggregation variable */
      }

      /* update the bounds of the aggregation variable y in x = a*y + c  ->  y = (x-c)/a */
      if( scalar > 0.0 )
      {
         if( SCIPsetIsInfinity(set, -var->glbdom.lb) )
            aggvarlb = -SCIPsetInfinity(set);
         else
            aggvarlb = (var->glbdom.lb - constant) / scalar;
         if( SCIPsetIsInfinity(set, var->glbdom.ub) )
            aggvarub = SCIPsetInfinity(set);
         else
            aggvarub = (var->glbdom.ub - constant) / scalar;
      }
      else
      {
         if( SCIPsetIsInfinity(set, -var->glbdom.lb) )
            aggvarub = SCIPsetInfinity(set);
         else
            aggvarub = (var->glbdom.lb - constant) / scalar;
         if( SCIPsetIsInfinity(set, var->glbdom.ub) )
            aggvarlb = -SCIPsetInfinity(set);
         else
            aggvarlb = (var->glbdom.ub - constant) / scalar;
      }
      aggvarlb = MAX(aggvarlb, aggvar->glbdom.lb);
      aggvarub = MIN(aggvarub, aggvar->glbdom.ub);
      SCIPvarAdjustLb(aggvar, set, &aggvarlb);
      SCIPvarAdjustUb(aggvar, set, &aggvarub);

      /* check the new bounds */
      if( SCIPsetIsGT(set, aggvarlb, aggvarub) )
      {
         /* the aggregation is infeasible */
         *infeasible = TRUE;
         return SCIP_OKAY;
      }
      else if( SCIPsetIsEQ(set, aggvarlb, aggvarub) )
      {
         /* the aggregation variable is fixed -> fix both variables */
         SCIP_CALL( SCIPvarFix(aggvar, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand,
               eventfilter, eventqueue, cliquetable, aggvarlb, infeasible, fixed) );
         if( !(*infeasible) )
         {
            SCIP_Bool varfixed;

            SCIP_CALL( SCIPvarFix(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand,
                  eventfilter, eventqueue, cliquetable, aggvarlb * scalar + constant, infeasible, &varfixed) );
            assert(*fixed == varfixed);
         }
         return SCIP_OKAY;
      }
      else
      {
         SCIP_Real oldbd;
         if( SCIPsetIsGT(set, aggvarlb, aggvar->glbdom.lb) )
         {
            oldbd = aggvar->glbdom.lb;
            SCIP_CALL( SCIPvarChgLbGlobal(aggvar, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, aggvarlb) );
            aggvarbdschanged = !SCIPsetIsEQ(set, oldbd, aggvar->glbdom.lb);
         }
         if( SCIPsetIsLT(set, aggvarub, aggvar->glbdom.ub) )
         {
            oldbd = aggvar->glbdom.ub;
            SCIP_CALL( SCIPvarChgUbGlobal(aggvar, blkmem, set, stat, lp, branchcand, eventqueue, cliquetable, aggvarub) );
            aggvarbdschanged = aggvarbdschanged || !SCIPsetIsEQ(set, oldbd, aggvar->glbdom.ub);
         }

         /* update the hole list of the aggregation variable */
         /**@todo update hole list of aggregation variable */
      }
   }
   while( aggvarbdschanged );

   SCIPsetDebugMsg(set, "  new bounds: <%s> [%g,%g]   <%s> [%g,%g]\n",
      var->name, var->glbdom.lb, var->glbdom.ub, aggvar->name, aggvar->glbdom.lb, aggvar->glbdom.ub);

   return SCIP_OKAY;
}

/** converts loose variable into aggregated variable */
SCIP_RETCODE SCIPvarAggregate(
   SCIP_VAR*             var,                /**< loose problem variable */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_SET*             set,                /**< global SCIP settings */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_PROB*            transprob,          /**< tranformed problem data */
   SCIP_PROB*            origprob,           /**< original problem data */
   SCIP_PRIMAL*          primal,             /**< primal data */
   SCIP_TREE*            tree,               /**< branch and bound tree */
   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTFILTER*     eventfilter,        /**< event filter for global (not variable dependent) events */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_VAR*             aggvar,             /**< loose variable y in aggregation x = a*y + c */
   SCIP_Real             scalar,             /**< multiplier a in aggregation x = a*y + c */
   SCIP_Real             constant,           /**< constant shift c in aggregation x = a*y + c */
   SCIP_Bool*            infeasible,         /**< pointer to store whether the aggregation is infeasible */
   SCIP_Bool*            aggregated          /**< pointer to store whether the aggregation was successful */
   )
{
   SCIP_VAR** vars;
   SCIP_Real* coefs;
   SCIP_Real* constants;
   SCIP_Real obj;
   SCIP_Real branchfactor;
   SCIP_Bool fixed;
   int branchpriority;
   int nlocksdown[NLOCKTYPES];
   int nlocksup[NLOCKTYPES];
   int nvbds;
   int i;
   int j;

   assert(var != NULL);
   assert(aggvar != NULL);
   assert(var->scip == set->scip);
   assert(var->glbdom.lb == var->locdom.lb); /*lint !e777*/
   assert(var->glbdom.ub == var->locdom.ub); /*lint !e777*/
   assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_LOOSE);
   assert(!SCIPeventqueueIsDelayed(eventqueue)); /* otherwise, the pseudo objective value update gets confused */
   assert(infeasible != NULL);
   assert(aggregated != NULL);

   *infeasible = FALSE;
   *aggregated = FALSE;

   /* get active problem variable of aggregation variable */
   SCIP_CALL( SCIPvarGetProbvarSum(&aggvar, set, &scalar, &constant) );

   /* aggregation is a fixing, if the scalar is zero */
   if( SCIPsetIsZero(set, scalar) )
   {
      SCIP_CALL( SCIPvarFix(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand, eventfilter,
            eventqueue, cliquetable, constant, infeasible, aggregated) );
      goto TERMINATE;
   }

   /* don't perform the aggregation if the aggregation variable is multi-aggregated itself */
   if( SCIPvarGetStatus(aggvar) == SCIP_VARSTATUS_MULTAGGR )
      return SCIP_OKAY;

   /**@todo currently we don't perform the aggregation if the aggregation variable has a non-empty hole list; this
    *  should be changed in the future
    */
   if( SCIPvarGetHolelistGlobal(var) != NULL )
      return SCIP_OKAY;

   /* if the variable is not allowed to be aggregated */
   if( SCIPvarDoNotAggr(var) )
   {
      SCIPsetDebugMsg(set, "variable is not allowed to be aggregated.\n");
      return SCIP_OKAY;
   }

   assert(aggvar->glbdom.lb == aggvar->locdom.lb); /*lint !e777*/
   assert(aggvar->glbdom.ub == aggvar->locdom.ub); /*lint !e777*/
   assert(SCIPvarGetStatus(aggvar) == SCIP_VARSTATUS_LOOSE);

   SCIPsetDebugMsg(set, "aggregate variable <%s>[%g,%g] == %g*<%s>[%g,%g] %+g\n", var->name, var->glbdom.lb, var->glbdom.ub,
      scalar, aggvar->name, aggvar->glbdom.lb, aggvar->glbdom.ub, constant);

   /* if variable and aggregation variable are equal, the variable can be fixed: x == a*x + c  =>  x == c/(1-a) */
   if( var == aggvar )
   {
      if( SCIPsetIsEQ(set, scalar, 1.0) )
         *infeasible = !SCIPsetIsZero(set, constant);
      else
      {
         SCIP_CALL( SCIPvarFix(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, branchcand,
               eventfilter, eventqueue, cliquetable, constant/(1.0-scalar), infeasible, aggregated) );
      }
      goto TERMINATE;
   }

   /* tighten the bounds of aggregated and aggregation variable */
   SCIP_CALL( varUpdateAggregationBounds(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp,
         branchcand, eventfilter, eventqueue, cliquetable, aggvar, scalar, constant, infeasible, &fixed) );
   if( *infeasible || fixed )
   {
      *aggregated = fixed;
      goto TERMINATE;
   }

   /* delete implications and variable bounds of the aggregated variable from other variables, but keep them in the
    * aggregated variable
    */
   SCIP_CALL( SCIPvarRemoveCliquesImplicsVbs(var, blkmem, cliquetable, set, FALSE, FALSE, FALSE) );

   /* set the aggregated variable's objective value to 0.0 */
   obj = var->obj;
   SCIP_CALL( SCIPvarChgObj(var, blkmem, set, transprob, primal, lp, eventqueue, 0.0) );

   /* unlock all locks */
   for( i = 0; i < NLOCKTYPES; i++ )
   {
      nlocksdown[i] = var->nlocksdown[i];
      nlocksup[i] = var->nlocksup[i];

      var->nlocksdown[i] = 0;
      var->nlocksup[i] = 0;
   }

   /* check, if variable should be used as NEGATED variable of the aggregation variable */
   if( SCIPvarIsBinary(var) && SCIPvarIsBinary(aggvar)
      && var->negatedvar == NULL && aggvar->negatedvar == NULL
      && SCIPsetIsEQ(set, scalar, -1.0) && SCIPsetIsEQ(set, constant, 1.0) )
   {
      /* link both variables as negation pair */
      var->varstatus = SCIP_VARSTATUS_NEGATED; /*lint !e641*/
      var->data.negate.constant = 1.0;
      var->negatedvar = aggvar;
      aggvar->negatedvar = var;

      /* copy donot(mult)aggr status */
      aggvar->donotaggr |= var->donotaggr;
      aggvar->donotmultaggr |= var->donotmultaggr;

      /* mark both variables to be non-deletable */
      SCIPvarMarkNotDeletable(var);
      SCIPvarMarkNotDeletable(aggvar);
   }
   else
   {
      /* convert variable into aggregated variable */
      var->varstatus = SCIP_VARSTATUS_AGGREGATED; /*lint !e641*/
      var->data.aggregate.var = aggvar;
      var->data.aggregate.scalar = scalar;
      var->data.aggregate.constant = constant;

      /* copy donot(mult)aggr status */
      aggvar->donotaggr |= var->donotaggr;
      aggvar->donotmultaggr |= var->donotmultaggr;

      /* mark both variables to be non-deletable */
      SCIPvarMarkNotDeletable(var);
      SCIPvarMarkNotDeletable(aggvar);
   }

   /* make aggregated variable a parent of the aggregation variable */
   SCIP_CALL( varAddParent(aggvar, blkmem, set, var) );

   /* relock the variable, thus increasing the locks of the aggregation variable */
   for( i = 0; i < NLOCKTYPES; i++ )
   {
      SCIP_CALL( SCIPvarAddLocks(var, blkmem, set, eventqueue, (SCIP_LOCKTYPE) i, nlocksdown[i], nlocksup[i]) );
   }

   /* move the variable bounds to the aggregation variable:
    *  - add all variable bounds again to the variable, thus adding it to the aggregation variable
    *  - free the variable bounds data structures
    */
   if( var->vlbs != NULL )
   {
      nvbds = SCIPvboundsGetNVbds(var->vlbs);
      vars = SCIPvboundsGetVars(var->vlbs);
      coefs = SCIPvboundsGetCoefs(var->vlbs);
      constants = SCIPvboundsGetConstants(var->vlbs);
      for( i = 0; i < nvbds && !(*infeasible); ++i )
      {
         SCIP_CALL( SCIPvarAddVlb(var, blkmem, set, stat, transprob, origprob, tree, reopt, lp, cliquetable, branchcand,
               eventqueue, vars[i], coefs[i], constants[i], FALSE, infeasible, NULL) );
      }
   }
   if( var->vubs != NULL )
   {
      nvbds = SCIPvboundsGetNVbds(var->vubs);
      vars = SCIPvboundsGetVars(var->vubs);
      coefs = SCIPvboundsGetCoefs(var->vubs);
      constants = SCIPvboundsGetConstants(var->vubs);
      for( i = 0; i < nvbds && !(*infeasible); ++i )
      {
         SCIP_CALL( SCIPvarAddVub(var, blkmem, set, stat, transprob, origprob, tree, reopt, lp, cliquetable, branchcand,
               eventqueue, vars[i], coefs[i], constants[i], FALSE, infeasible, NULL) );
      }
   }
   SCIPvboundsFree(&var->vlbs, blkmem);
   SCIPvboundsFree(&var->vubs, blkmem);

   /* move the implications to the aggregation variable:
    *  - add all implications again to the variable, thus adding it to the aggregation variable
    *  - free the implications data structures
    */
   if( var->implics != NULL && SCIPvarGetType(aggvar) == SCIP_VARTYPE_BINARY )
   {
      assert(SCIPvarIsBinary(var));
      for( i = 0; i < 2; ++i )
      {
         SCIP_VAR** implvars;
         SCIP_BOUNDTYPE* impltypes;
         SCIP_Real* implbounds;
         int nimpls;

         nimpls = SCIPimplicsGetNImpls(var->implics, (SCIP_Bool)i);
         implvars = SCIPimplicsGetVars(var->implics, (SCIP_Bool)i);
         impltypes = SCIPimplicsGetTypes(var->implics, (SCIP_Bool)i);
         implbounds = SCIPimplicsGetBounds(var->implics, (SCIP_Bool)i);

         for( j = 0; j < nimpls && !(*infeasible); ++j )
         {
            /* @todo can't we omit transitive closure, because it should already have been done when adding the
             *       implication to the aggregated variable?
             */
            SCIP_CALL( SCIPvarAddImplic(var, blkmem, set, stat, transprob, origprob, tree, reopt, lp, cliquetable,
                  branchcand, eventqueue, (SCIP_Bool)i, implvars[j], impltypes[j], implbounds[j], FALSE, infeasible,
                  NULL) );
            assert(nimpls == SCIPimplicsGetNImpls(var->implics, (SCIP_Bool)i));
         }
      }
   }
   SCIPimplicsFree(&var->implics, blkmem);

   /* add the history entries to the aggregation variable and clear the history of the aggregated variable */
   SCIPhistoryUnite(aggvar->history, var->history, scalar < 0.0);
   SCIPhistoryUnite(aggvar->historycrun, var->historycrun, scalar < 0.0);
   SCIPhistoryReset(var->history);
   SCIPhistoryReset(var->historycrun);

   /* update flags of aggregation variable */
   aggvar->removable &= var->removable;

   /* update branching factors and priorities of both variables to be the maximum of both variables */
   branchfactor = MAX(aggvar->branchfactor, var->branchfactor);
   branchpriority = MAX(aggvar->branchpriority, var->branchpriority);
   SCIP_CALL( SCIPvarChgBranchFactor(aggvar, set, branchfactor) );
   SCIP_CALL( SCIPvarChgBranchPriority(aggvar, branchpriority) );
   SCIP_CALL( SCIPvarChgBranchFactor(var, set, branchfactor) );
   SCIP_CALL( SCIPvarChgBranchPriority(var, branchpriority) );

   /* update branching direction of both variables to agree to a single direction */
   if( scalar >= 0.0 )
   {
      if( (SCIP_BRANCHDIR)var->branchdirection == SCIP_BRANCHDIR_AUTO )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(var, (SCIP_BRANCHDIR)aggvar->branchdirection) );
      }
      else if( (SCIP_BRANCHDIR)aggvar->branchdirection == SCIP_BRANCHDIR_AUTO )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(aggvar, (SCIP_BRANCHDIR)var->branchdirection) );
      }
      else if( var->branchdirection != aggvar->branchdirection )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(var, SCIP_BRANCHDIR_AUTO) );
      }
   }
   else
   {
      if( (SCIP_BRANCHDIR)var->branchdirection == SCIP_BRANCHDIR_AUTO )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(var, SCIPbranchdirOpposite((SCIP_BRANCHDIR)aggvar->branchdirection)) );
      }
      else if( (SCIP_BRANCHDIR)aggvar->branchdirection == SCIP_BRANCHDIR_AUTO )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(aggvar, SCIPbranchdirOpposite((SCIP_BRANCHDIR)var->branchdirection)) );
      }
      else if( var->branchdirection != aggvar->branchdirection )
      {
         SCIP_CALL( SCIPvarChgBranchDirection(var, SCIP_BRANCHDIR_AUTO) );
      }
   }

   if( var->probindex != -1 )
   {
      /* inform problem about the variable's status change */
      SCIP_CALL( SCIPprobVarChangedStatus(transprob, blkmem, set, branchcand, cliquetable, var) );
   }

   /* reset the objective value of the aggregated variable, thus adjusting the objective value of the aggregation
    * variable and the problem's objective offset
    */
   SCIP_CALL( SCIPvarAddObj(var, blkmem, set, stat, transprob, origprob, primal, tree, reopt, lp, eventfilter, eventqueue, obj) );

   /* issue VARFIXED event */
   SCIP_CALL( varEventVarFixed(var, blkmem, set, eventqueue, 1) );

   *aggregated = TRUE;

TERMINATE:
   /* check aggregation on debugging solution */
   if( *infeasible || *aggregated )
      SCIP_CALL( SCIPdebugCheckAggregation(set, var, &aggvar, &scalar, constant, 1) ); /*lint !e506 !e774*/

   return SCIP_OKAY;
}

/** Tries to aggregate an equality a*x + b*y == c consisting of two (implicit) integral active problem variables x and
 *  y. An integer aggregation (i.e. integral coefficients a' and b', such that a'*x + b'*y == c') is searched.
 *
 *  This can lead to the detection of infeasibility (e.g. if c' is fractional), or to a rejection of the aggregation
 *  (denoted by aggregated == FALSE), if the resulting integer coefficients are too large and thus numerically instable.
 */
static
SCIP_RETCODE tryAggregateIntVars(
   SCIP_SET*             set,                /**< global SCIP settings */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_STAT*            stat,               /**< problem statistics */
   SCIP_PROB*            transprob,          /**< tranformed problem data */
   SCIP_PROB*            origprob,           /**< original problem data */
   SCIP_PRIMAL*          primal,             /**< primal data */
   SCIP_TREE*            tree,               /**< branch and bound tree */
   SCIP_REOPT*           reopt,              /**< reoptimization data structure */
   SCIP_LP*              lp,                 /**< current LP data */
   SCIP_CLIQUETABLE*     cliquetable,        /**< clique table data structure */
   SCIP_BRANCHCAND*      branchcand,         /**< branching candidate storage */
   SCIP_EVENTFILTER*     eventfilter,        /**< event filter for global (not variable dependent) events */
   SCIP_EVENTQUEUE*      eventqueue,         /**< event queue */
   SCIP_VAR*             varx,               /**< integral variable x in equality a*x + b*y == c */
   SCIP_VAR*             vary,               /**< integral variable y in equality a*x + b*y == c */
   SCIP_Real             scalarx,            /**< multiplier a in equality a*x + b*y == c */
   SCIP_Real             scalary,            /**< multiplier b in equality a*x + b*y == c */
   SCIP_Real             rhs,                /**< right hand side c in equality a*x + b*y == c */
   SCIP_Bool*            infeasible,         /**< pointer to store whether the aggregation is infeasible */
   SCIP_Bool*            aggregated          /**< pointer to store whether the aggregation was successful */
   )
{
   SCIP_VAR* aggvar;
   char aggvarname[SCIP_MAXSTRLEN];
   SCIP_Longint scalarxn = 0;
   SCIP_Longint scalarxd = 0;
   SCIP_Longint scalaryn = 0;
   SCIP_Longint scalaryd = 0;
   SCIP_Longint a;
   SCIP_Longint b;
   SCIP_Longint c;
   SCIP_Longint scm;
   SCIP_Longint gcd;
   SCIP_Longint currentclass;
   SCIP_Longint classstep;
   SCIP_Longint xsol;
   SCIP_Longint ysol;
   SCIP_Bool success;
   SCIP_VARTYPE vartype;

#define MAXDNOM 1000000LL

   assert(set != NULL);
   assert(blkmem != NULL);
   assert(stat != NULL);
   assert(transprob != NULL);
   assert(origprob != NULL);
   assert(tree != NULL);
   assert(lp != NULL);
   assert(cliquetable != NULL);
   assert(branchcand != NULL);
   assert(eventqueue != NULL);
   assert(varx != NULL);
   assert(vary != NULL);
   assert(varx != vary);
   assert(infeasible != NULL);
   assert(aggregated != NULL);
   assert(SCIPsetGetStage(set) == SCIP_STAGE_PRESOLVING);
   assert(SCIPvarGetStatus(varx) == SCIP_VARSTATUS_LOOSE);
   assert(SCIPvarGetType(varx) == SCIP_VARTYPE_INTEGER || SCIPvarGetType(varx) == SCIP_VARTYPE_IMPLINT);
   assert(SCIPvarGetStatus(vary) == SCIP_VARSTATUS_LOOSE);
   assert(SCIPvarGetType(vary) == SCIP_VARTYPE_INTEGER || SCIPvarGetType(vary) == SCIP_VARTYPE_IMPLINT);
   assert(!SCIPsetIsZero(set, scalarx));
   assert(!SCIPsetIsZero(set, scalary));

   *infeasible = FALSE;
   *aggregated = FALSE;

   /* if the variable is not allowed to be aggregated */
   if( SCIPvarDoNotAggr(varx) )
   {
      SCIPsetDebugMsg(set, "variable is not allowed to be aggregated.\n");
      return SCIP_OKAY;
   }

   /* get rational representation of coefficients */
   success = SCIPrealToRational(scalarx, -SCIPsetEpsilon(set), SCIPsetEpsilon(set), MAXDNOM, &scalarxn, &scalarxd);
   if( success )
      success = SCIPrealToRational(scalary, -SCIPsetEpsilon(set), SCIPsetEpsilon(set), MAXDNOM, &scalaryn, &scalaryd);
   if( !success )
      return SCIP_OKAY;
   assert(scalarxd >= 1);
   assert(scalaryd >= 1);

   /* multiply equality with smallest common denominator */
   scm = SCIPcalcSmaComMul(scalarxd, scalaryd);
   a = (scm/scalarxd)*scalarxn;
   b = (scm/scalaryd)*scalaryn;
   rhs *= scm;

   /* divide equality by the greatest common divisor of a and b */
   gcd = SCIPcalcGreComDiv(ABS(a), ABS