We propose a novel constraint-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 w.r.t. 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 large initial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of girth and diameter. With our approach, we could confirm the Simon-Murty Conjecture (1979) on diameter-2-critical graphs for graphs up to 18 vertices.
@InProceedings{kirchweger_et_al:LIPIcs.CP.2021.34, author = {Kirchweger, Markus and Szeider, Stefan}, title = {{SAT Modulo Symmetries for Graph Generation}}, booktitle = {27th International Conference on Principles and Practice of Constraint Programming (CP 2021)}, pages = {34:1--34:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-211-2}, ISSN = {1868-8969}, year = {2021}, volume = {210}, editor = {Michel, Laurent D.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.34}, URN = {urn:nbn:de:0030-drops-153257}, doi = {10.4230/LIPIcs.CP.2021.34}, annote = {Keywords: symmetry breaking, SAT encodings, graph generation, combinatorial search, extremal graphs, CDCL} }
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