Breaking Symmetries in Graph Representation

There are many complex combinatorial problems which involve searching for an undirected graph satisfying a certain property. These problems are often highly challenging because of the large number of isomorphic representations of a possible solution. In this paper we introduce novel, effective and compact, symmetry breaking constraints for undirected graph search. While incomplete, these prove highly beneficial in pruning the search for a graph. We illustrate the application of symmetry breaking in graph representation to resolve several open instances in extremal graph theory

Logic Programming with Max-Clique and its Application to Graph Coloring (Tool Description)

This paper presents pl-cliquer, a Prolog interface to the cliquer tool for the maximum clique problem. Using pl-cliquer facilitates a programming style that allows logic programs to integrate with other tools such as: Boolean satisfiability solvers, finite domain constraint solvers, and graph isomorphism tools. We illustrate this programming style to solve the Graph Coloring problem, applying a symmetry break that derives from finding a maximum clique in the input graph. We present an experimentation of the resulting Graph Coloring solver on two benchmarks, one from the graph coloring community and the other from the examination timetabling community. The implementation of pl-cliquer consists of two components: A lightweight C interface, connecting cliquer\u27s C library and Prolog, and a Prolog module which loads the library. The complete tool is available as a SWI-Prolog module