Dynamic symmetry breaking for SAT-encodings of combinatorial problems

Abstract

We propose a novel SAT-based approach to graph generation. Our approach utilizes the interaction between a CDCL SAT solver and a special symmetry propagator where the SAT solver runs on an encoding of the desired graph property. The symmetry propagator checks partially generated graphs for minimality with respect to a lexicographic ordering during the solving process. This approach has several advantages over a static symmetry breaking: (i) symmetries are detected early in the generation process, (ii) symmetry breaking is seamlessly integrated into the CDCL procedure, and (iii) the propagator can perform a complete symmetry breaking without causing a prohibitively largeinitial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of forbidden subgraphs and diameter. With our approach, we could confirm the Murty-Simon Conjecture (1979) on diameter-2-critical graphs for graphs up to 19 vertices and prove the completeness of sets of Ramsey graphs with certain parameters.