# SCIP

Solving Constraint Integer Programs

cons_storeGraph.h File Reference

## Detailed Description

constraint handler for storing the graph at each node of the tree

This file implements the constraints that are used for the branching in the coloring algorithm.

For each node in the branch-and-bound tree, a constraint of this type is created, which stores all restrictions related to that branch-and-bound node.

First of all, it stores the type of the constraint ("same" or "differ", the root has type root) and the two nodes in the graph on which this restriction is applied. When the branch-and-bound node corresponding to the constraint is examined for the first time, the constraint creates a graph that takes into account all the restrictions, which are active at this node. At the root, this is the original (preprocessed) graph. At any other branch-and-bound node, it takes the graph of the constraint related to the branch-and-bound father of the current node and modifies it so that all restrictions up to this node are respected. Since the graph in the branch-and-bound father respects all restrictions on the path to that node, only the last requirement, the one saved at the current branch-and-bound node, must be added. This is done as follows: Adding a DIFFER(v,w) constraint is easy, since it suffices to add an edge between v and w. For a SAME(v,w) constraint, the original idea is to collapse the nodes v and w into one single vertex. Since this is not possible in the tclique-graph data structure, we introduce new edges in the graph, so that v and w have the same neighborhood. Hence, in the pricing routine, each new stable set will either contain both nodes or none of them, since we create (inclusion-) maximal sets.

This does of course not hold for sets created in a higher level of the branch-and-bound tree or in another subtree. In order to forbid all of these sets, which do not fulfill the current restrictions, a propagation is started when the node is entered the first time and repeated later, if the node is reentered after the creation of new variables in another subtree. The propagation simply fixes to 0 all variables representing a stable set that does not fulfill the restriction at the current node.

The information about all fusions of nodes (caused by the SAME() operation) is stored, so that the nodes constituting a union can be accessed easily. Each union has a representative and a set of nodes, whereas each node knows the representative of the union it belongs to. At the beginning, each node forms its own union and therefore each node also represents this union, consisting of only this node. Later on, some nodes represent unions of several nodes, while other nodes are part of a union which they do not represent, so they have another node as representative. The representatives of the nodes are returned by the methods COLORconsGetRepresentative() / COLORconsGetRepresentatives(), the union represented by a node is returned by COLORconsGetUnion(), the array of unions, indexed by the representing node, is returned by COLORconsGetUnions().

Definition in file cons_storeGraph.h.

#include "scip/scip.h"
#include "tclique/tclique.h"

Go to the source code of this file.

## Typedefs

typedef enum COLOR_ConsType COLOR_CONSTYPE

## Enumerations

enum  COLOR_ConsType {
COLOR_CONSTYPE_DIFFER = 0,
COLOR_CONSTYPE_SAME = 1,
COLOR_CONSTYPE_ROOT = 2
}

## Functions

SCIP_CONSCOLORconsGetActiveStoreGraphConsFromHandler (SCIP_CONSHDLR *conshdlr)

SCIP_CONSCOLORconsGetActiveStoreGraphCons (SCIP *scip)

int * COLORconsGetRepresentatives (SCIP *scip)

TCLIQUE_GRAPHCOLORconsGetCurrentGraph (SCIP *scip)

TCLIQUE_GRAPHCOLORconsGetComplementaryGraph (SCIP *scip)

int COLORconsGetRepresentative (SCIP *scip, int node)

void COLORconsGetUnions (SCIP *scip, int ***unions, int **lengths)

void COLORconsGetUnion (SCIP *scip, int **unionSet, int *length, int node)

SCIP_RETCODE COLORincludeConshdlrStoreGraph (SCIP *scip)

SCIP_RETCODE COLORcreateConsStoreGraph (SCIP *scip, SCIP_CONS **cons, const char *name, SCIP_CONS *fatherconstraint, COLOR_CONSTYPE type, int node1, int node2, SCIP_NODE *stickingnode)

void COLORconsGetStack (SCIP *scip, SCIP_CONS ***stack, int *nstackelements)

## ◆ COLOR_CONSTYPE

 typedef enum COLOR_ConsType COLOR_CONSTYPE

Definition at line 76 of file cons_storeGraph.h.

## ◆ COLOR_ConsType

 enum COLOR_ConsType
Enumerator
COLOR_CONSTYPE_DIFFER
COLOR_CONSTYPE_SAME
COLOR_CONSTYPE_ROOT

Definition at line 70 of file cons_storeGraph.h.

## ◆ COLORconsGetActiveStoreGraphConsFromHandler()

 SCIP_CONS* COLORconsGetActiveStoreGraphConsFromHandler ( SCIP_CONSHDLR * conshdlr )

returns the store graph constraint of the current node, needs the pointer to the constraint handler

Parameters
 conshdlr constaint handler for store-graph constraints

Definition at line 842 of file cons_storeGraph.c.

References COLORconsGetActiveStoreGraphCons(), NULL, and SCIPconshdlrGetData().

Referenced by COLORcreateConsStoreGraph().

## ◆ COLORconsGetActiveStoreGraphCons()

 SCIP_CONS* COLORconsGetActiveStoreGraphCons ( SCIP * scip )

returns the store graph constraint of the current node, needs only the pointer to scip

returns the store graph constraint of the current node, only needs the pointer to scip

Parameters
 scip SCIP data structure

Definition at line 858 of file cons_storeGraph.c.

## ◆ COLORconsGetRepresentatives()

 int* COLORconsGetRepresentatives ( SCIP * scip )

returns array of representatives of all nodes

Parameters
 scip SCIP data structure

Definition at line 941 of file cons_storeGraph.c.

Referenced by COLORconsGetComplementaryGraph().

## ◆ COLORconsGetCurrentGraph()

 TCLIQUE_GRAPH* COLORconsGetCurrentGraph ( SCIP * scip )

returns the current graph

Parameters
 scip SCIP data structure

Definition at line 882 of file cons_storeGraph.c.

## ◆ COLORconsGetComplementaryGraph()

 TCLIQUE_GRAPH* COLORconsGetComplementaryGraph ( SCIP * scip )

returns the complementary graph

Parameters
 scip SCIP data structure

Definition at line 910 of file cons_storeGraph.c.

Referenced by COLORconsGetCurrentGraph(), and SCIP_DECL_PRICERREDCOST().

## ◆ COLORconsGetRepresentative()

 int COLORconsGetRepresentative ( SCIP * scip, int node )

returns representative of the union which contains a given node

returns the representative of the union which contains a given node

Parameters
 scip SCIP data structure node the node, for wich the representative is searched

Definition at line 969 of file cons_storeGraph.c.

## ◆ COLORconsGetUnions()

 void COLORconsGetUnions ( SCIP * scip, int *** unions, int ** lengths )

returns array of all unions, a union is saved in the array at the position of its representative

returns the array of all unions, a union is saved in the array at the position of its representative

Parameters
 scip SCIP data structure unions output: array containing array which contains nodes in the union lengths output: lengths of the unions

Definition at line 1002 of file cons_storeGraph.c.

Referenced by COLORconsGetRepresentative().

## ◆ COLORconsGetUnion()

 void COLORconsGetUnion ( SCIP * scip, int ** nodesinunion, int * nnodesinunion, int node )

returns the union which has a given node as representative

Parameters
 scip SCIP data structure nodesinunion output: array containig nodes in the union nnodesinunion output: length of the union node the node, whose union we want to get

Definition at line 1034 of file cons_storeGraph.c.

Referenced by COLORconsGetUnions().

## ◆ COLORincludeConshdlrStoreGraph()

 SCIP_RETCODE COLORincludeConshdlrStoreGraph ( SCIP * scip )

creates the handler for graph storing constraints and includes it in SCIP

creates the handler for storeGraph constraints and includes it in SCIP

Parameters
 scip SCIP data structure

Definition at line 746 of file cons_storeGraph.c.

Referenced by SCIP_DECL_CONSPROP(), and SCIPincludeColoringPlugins().

## ◆ COLORcreateConsStoreGraph()

 SCIP_RETCODE COLORcreateConsStoreGraph ( SCIP * scip, SCIP_CONS ** cons, const char * name, SCIP_CONS * fatherconstraint, COLOR_CONSTYPE type, int node1, int node2, SCIP_NODE * stickingnode )

creates and captures a storeGraph constraint, uses knowledge of the B&B-father

Parameters
 scip SCIP data structure cons pointer to hold the created constraint name name of constraint fatherconstraint constraint in B&B-father type type of the constraint: COLOR_CONSTYPE_SAME or COLOR_CONSTYPE_DIFFER node1 the first node of the constraint node2 the second node of the constraint stickingnode the B&B-tree node at which the constraint will be sticking

Definition at line 781 of file cons_storeGraph.c.

## ◆ COLORconsGetStack()

 void COLORconsGetStack ( SCIP * scip, SCIP_CONS *** stack, int * nstackelements )

returns the stack and the number of elements on it

Parameters
 scip SCIP data structure stack return value: pointer to the stack nstackelements return value: pointer to int, for number of elements on the stack

Definition at line 1065 of file cons_storeGraph.c.

References NULL, SCIPconshdlrGetData(), SCIPerrorMessage, and SCIPfindConshdlr().

Referenced by COLORconsGetUnion().