^V\}.] Suppose a user wants to implement a constraint handler `cons_stableset`

that enforces a solution to define a stable set in \(G\), e.g., by propagation methods and separating edge and clique inequalities. Then, the symmetries of the constraint are the weight-preserving automorphisms of the underlying graph \(G\). The symmetry detection graph thus can be almost a copy of \(G\).

In our construction, we introduce for each node \(v\) of the graph an operator node \(v'\). Moreover, for each edge \(\{u,v\}\in E\), we add the edges \(\{u',v'\}\) to the symmetry detection graph. To identify the symmetry detection graph as derived from `cons_stableset`

, we add a constraint node that is connected with all operator nodes, which preserves the automorphisms of \(G\). Finally, each node \(v'\) is connected with the corresponding variable node for \(x_v\) by an edge.

In the following, we present a code snippet showing how to implement the above mentioned symmetry detection graph. We assume that the constraint data `consdata`

contains the following fields

`nnodes`

number of nodes in graph;`nedges`

number of edges in graph;`first`

array containing the first nodes of each edge;`second`

array containing the second nodes of each edge;`weights`

array containing for each node its corresponding weight;`vars`

array containing a binary variable for each node modeling whether node is present in stable set.

The code for creating the symmetry detection callback could then look like this.

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