Abstract
Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has sets of equivalent solutions in which the three colours are permuted. Symmetry in CSPs can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered. If a partial assignment does not lead to a solution, neither will any symmetrically equivalent assignment. When searching for all solutions, for every solution found, all the symmetrically equivalent solutions will also be found.
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References
Fahle, T., Schamberger, S., Sellmann, M.: Symmetry Breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 225–239. Springer, Heidelberg (2001)
Focacci, F., Milano, M.: Global Cut Framework for Removing Symmetries. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 77–92. Springer, Heidelberg (2001)
Gallian, J.A.: A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, DS6 (2002), http://www.combinatorics.org/Surveys
The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.3 (2002), http://www.gap-system.org
Gent, I.P., Harvey, W., Kelsey, T.: Groups and Constraints: Symmetry Breaking during Search. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 415–430. Springer, Heidelberg (2002)
Gent, I.P., Harvey, W., Kelsey, T., Linton, S.: Generic SBDD using Computational Group Theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)
Gent, P., Smith, B.M.: Symmetry Breaking During Search in Constraint Programming. In: Horn, W. (ed.) Proceedings ECAI 2000, pp. 599–603 (2000)
Lustig, J., Puget, J.-F.: Program Does Not Equal Program: Constraint Programming and Its Relationship to Mathematical Programming. INTERFACES 31(6), 29–53 (2001)
Petrie, K.E., Smith, B.M.: Symmetry Breaking in Graceful Graphs. Technical Report APES-56a-2003, APES Research Group (June 2003), Available from http://www.dcs.st-and.ac.uk/~apes/apesreports.html
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Petrie, K.E., Smith, B.M. (2003). Symmetry Breaking in Graceful Graphs. In: Rossi, F. (eds) Principles and Practice of Constraint Programming – CP 2003. CP 2003. Lecture Notes in Computer Science, vol 2833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45193-8_81
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DOI: https://doi.org/10.1007/978-3-540-45193-8_81
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