Abstract
Symmetry breaking is an essential component when solving graph search problems as it restricts the search space to that of canonical representations. There are an abundance of powerful tools, such as nauty, which apply to find the canonical representation of a given graph and to test for isomorphisms given a set of graphs. In contrast, for graph search problems, current symmetry breaking techniques are partial and solvers unnecessarily explore an abundance of isomorphic parts of the search space. This paper is novel in that it introduces complete symmetry breaking for graph search problems by modeling, in terms of constraints, the same ideas underlying the algorithm applied in tools like nauty. Whereas nauty tests given graphs, symmetry breaks restrict the search space and apply during generation.
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Read, R.C.: Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations. Ann. Discrete Math. 2, 107–120 (1978)
Jäger, G., Arnold, F.: SAT and IP based algorithms for magic labeling including a complete search for total magic labelings. J. Discrete Algorithms 31, 87–103 (2015)
Puget, J.: On the satisfiability of symmetrical constrained satisfaction problems. In: Methodologies for Intelligent Systems, 7th International Symposium, ISMIS 1993, Trondheim, Norway, 15–18 June 1993, Proceedings, pp. 350–361 (1993)
Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR 1996), Cambridge, Massachusetts, USA, 5–8 November 1996, pp. 148–159 (1996)
Shlyakhter, I.: Generating effective symmetry-breaking predicates for search problems. Discrete Appl. Math. 155(12), 1539–1548 (2007)
Walsh, T.: General symmetry breaking constraints. In: Principles and Practice of Constraint Programming - Cp. 2006, 12th International Conference, Cp. 2006, Nantes, France, 25–29 September 2006, Proceedings, pp. 650–664 (2006)
Gent, I.P., Smith, B.M.: Symmetry breaking in constraint programming. In: Horn, W. (ed.) ECAI 2000, Proceedings of the 14th European Conference on Artificial Intelligence, Berlin, Germany, 20–25 August 2000, pp. 599–603. IOS Press (2000)
Mears, C., de la Banda, G., Demoen, B., Wallace, M.: Lightweight dynamic symmetry breaking. Constraints 19(3), 195–242 (2013)
McKay, B.D.: Practical graph isomorphism. Congressus Numerantium 30, 45–87 (1981)
Junttila, T., Kaski, P.: Engineering an efficient canonical labeling tool for large and sparse graphs. In: Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments, SIAM, pp. 135–149 (2007)
Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting structure in symmetry detection for CNF
Itzhakov, A., Codish, M.: Breaking symmetries in graph search with canonizing sets. Constraints 21, 1–18 (2016)
Metodi, A., Codish, M., Stuckey, P.J.: Boolean equi-propagation for concise and efficient SAT encodings of combinatorial problems. J. Artif. Intell. Res. (JAIR) 46, 303–341 (2013)
Audemard, G., Simon, L.: Glucose 4.0 SAT Solver. http://www.labri.fr/perso/lsimon/glucose/
Gebser, M., Kaufmann, B., Schaub, T.: Conflict-driven answer set solving: from theory to practice. Artif. Intell. 187, 52–89 (2012)
Erdös, P., Gallai, T.: Graphs with prescribed degrees of vertices (in Hungarian). Mat. Lapok 11, 264–274 (1960). http://www.renyi.hu/~p_erdos/1961-05.pdf
McKay, B.D., Piperno, A.: Practical graph isomorphism II. J. Symbolic Comput. 60, 94–112 (2014)
Codish, M., Miller, A., Prosser, P., Stuckey, P.J.: Breaking symmetries in graph representation. In: Rossi, F. (ed.) Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, IJCAI/AAAI (2013)
Sloane, N.J.A. (ed.): The On-Line Encyclopedia of Integer Sequences. https://oeis.org Accessed April 2016
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Codish, M., Gange, G., Itzhakov, A., Stuckey, P.J. (2016). Breaking Symmetries in Graphs: The Nauty Way. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_11
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DOI: https://doi.org/10.1007/978-3-319-44953-1_11
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