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Dynamic structural symmetry breaking for constraint satisfaction problems

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Abstract

In recent years, symmetry breaking for constraint satisfaction problems (CSPs) has attracted considerable attention. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value or variable interchangeability is tractable using dedicated search procedures. We also show the limits of efficient symmetry breaking for such dominance-detection schemes by proving intractability results for some classes of CSPs.

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References

  1. Ahuja, R., Magnati, T., & Orlin, J. (1993). Network flows. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  2. Backofen, R., & Will, S. (1999). Excluding symmetries in constraint-based search. In J. Jaffar (Ed.), Proceedings of CP’99, LNCS (Vol. 1713, pp. 73–87). New York: Springer.

    Google Scholar 

  3. Barnier, N., & Brisset, P. (2002). Solving the Kirkman’s schoolgirl problem in a few seconds. In P. Van Hentenryck (Ed.), Proceedings of CP’02, LNCS (Vol. 2470. pp. 477–491). New York: Springer.

    Google Scholar 

  4. Cameron, P. (1999). Permutation groups. Number 45 in London Mathematical Society Student Texts. Cambridge: Cambridge University Press.

    Google Scholar 

  5. Cohen, D. A., Jeavons, P., Jefferson, C., Petrie, K. E., & Smith, B. M. (2005). Symmetry definitions for constraint satisfaction problems. In P. van Beek (Ed.) Proceedings of CP’05, LNCS (Vol. 3709, pp. 17–31). New York: Springer.

    Google Scholar 

  6. Colbourn, C. J., & Dinitz, J. H. (Eds.) (1996). The CRC handbook of combinatorial designs. Boca Raton: CRC.

    MATH  Google Scholar 

  7. Crawford, J. M., Ginsberg, M., Luks, E., & Roy, A. (1996). Symmetry-breaking predicates for search problems. In L. C. Aiello, J. Doyle, & S. C. Shapiro (Eds.), Proceedings of KR’96 (pp. 148–159). San Francisco: Morgan Kaufmann.

    Google Scholar 

  8. Er, M. C. (1988). A fast algorithm for generating set partitions. The Computer Journal, 31(3), 283–284.

    Article  MATH  Google Scholar 

  9. Fahle, T., Schamberger, S., & Sellmann, M. (2001). Symmetry breaking. In T. Walsh (Ed.), Proceedings of CP’01, LNCS (Vol. 2239, pp. 93–107). New York: Springer.

    Google Scholar 

  10. Flener, P., Frisch, A. M., Hnich, B., Kızıltan, Z., Miguel, I., Pearson, J., et al. (2001). Symmetry in matrix models. In P. Flener & J. Pearson (Eds.), Proceedings of SymCon’01. http://www.it.uu.se/research/group/astra/SymCon01/.

  11. Flener, P., Frisch, A. M., Hnich, B., Kızıltan, Z., Miguel, I., Pearson, J., et al. (2002). Breaking row and column symmetries in matrix models. In P. Van Hentenryck (Ed.), Proceedings of CP’02, LNCS (Vol. 2470, pp. 462–476). New York: Springer.

    Google Scholar 

  12. Flener, P., Pearson, J., Sellmann, M., & Van Hentenryck, P. (2006). Static and dynamic structural symmetry breaking. In F. Benhamou (Ed.), Proceedings of CP’06, LNCS (Vol. 4204, pp. 695–699). New York: Springer.

    Google Scholar 

  13. Flener, P., Pearson, J., & Sellmann, M. (2008). Static and dynamic structural symmetry breaking. Technical Report 2008-023, Department of Information Technology, Uppsala University, Sweden, September. http://www.it.uu.se/research/reports/2008-023/.

  14. Flener, P., Pearson, J., Sellmann, M., & Ågren, M. (2007). Structural symmetry breaking for constraint satisfaction problems. Technical Report 2007-032, Department of Information Technology, Uppsala University, Sweden, November. http://www.it.uu.se/research/reports/2007-032/.

  15. Focacci, F., & Milano, M. (2001). Global cut framework for removing symmetries. In T. Walsh (Ed.), Proceedings of CP’01, LNCS (Vol. 2239, pp. 77–92). New York: Springer.

    Google Scholar 

  16. Freuder, E. C. (1991). Eliminating interchangeable values in constraint satisfaction problems. In Proceedings of AAAI’91 (pp. 227–233). Menlo Park: AAAI.

    Google Scholar 

  17. Gent, I. P., & Smith, B. M. (2000). Symmetry breaking during search in constraint programming. In Proceedings of ECAI’00 (pp. 599–603). Amsterdam: IOS.

    Google Scholar 

  18. Heller, D. S., & Sellmann, M. (2006). Dynamic symmetry breaking restarted. In F. Benhamou (Ed.), Proceedings of CP’06, LNCS (Vol. 4204, pp. 721–725). New York: Springer.

    Google Scholar 

  19. Kubale, M., & Jackowski, B. (1985). A generalized implicit enumeration algorithm for graph coloring. CACM, 28(4), 412–418.

    Google Scholar 

  20. Law, Y., & Lee, J. (2006). Symmetry breaking constraints for value symmetries in constraint satisfaction. Constraints, 11(2–3), 221–267.

    Article  MATH  MathSciNet  Google Scholar 

  21. Law, Y., Lee, J., Walsh, T., & Yip, J. (2007). Breaking symmetry of interchangeable variables and values. In C. Bessière (Ed.), Proceedings of CP’07, LNCS (Vol. 4741, pp. 423–437). New York: Springer.

    Google Scholar 

  22. Meseguer, P., & Torras, C. (2001). Exploiting symmetries within constraint satisfaction search. Artificial Intelligence, 129(1–2), 133–163.

    Article  MATH  MathSciNet  Google Scholar 

  23. Puget, J.-F. (1993). On the satisfiability of symmetrical constrained satisfaction problems. In J. Komorowski & Z. Raś (Ed.), Proceedings of ISMIS’93, LNAI (Vol. 689, pp. 350–361). New York: Springer.

    Google Scholar 

  24. Puget, J.-F. (2002). Symmetry breaking revisited. In P. Van Hentenryck (Ed.), Proceedings of CP’02, LNCS (Vol. 2470, pp. 446–461). New York: Springer.

    Google Scholar 

  25. Puget, J.-F. (2006). An efficient way of breaking value symmetries. In Proceedings of AAAI’06. Menlo Park: AAAI.

    Google Scholar 

  26. Roney-Dougal, C. M., Gent, I. P., Kelsey, T., & Linton, S. (2004). Tractable symmetry breaking using restricted search trees. In R. L. de Mántaras & L. Saitta (Eds.), Proceedings of ECAI’04 (pp. 211–215). Amsterdam: IOS.

    Google Scholar 

  27. Sellmann, M., & Van Hentenryck, P. (2005). Structural symmetry breaking. In Proceedings of IJCAI’05 (pp. 298–303). IJCAI.

  28. Sellmann, M., Gellermann, T., & Wright, R. (2007). Cost-based filtering for shorter path constraints. Constraints, 12(2), 207–238.

    Article  MATH  MathSciNet  Google Scholar 

  29. Shlyakhter, I. (2001). Generating effective symmetry-breaking predicates for search problems. Electronic Notes in Discrete Mathematics (Vol. 9). Proceedings of SAT’01.

  30. Smith, B. M. (2001). Reducing symmetry in a combinatorial design problem. In C. Gervet & M. Wallace (Eds.), Proceedings of CP-AI-OR’01.

  31. Smith, B. M., Brailsford, S. C., Hubbard, P. M., & Williams, H. P. (1996). The progressive party problem: Integer linear programming and constraint programming compared. Constraints, 1, 119–138.

    Article  MathSciNet  Google Scholar 

  32. Van Hentenryck, P. (2002). Constraint and integer programming in OPL. INFORMS Journal on Computing, 14(4), 345–372.

    Article  MathSciNet  Google Scholar 

  33. Van Hentenryck, P., Flener, P., Pearson, J., & Ågren, M. (2003). Tractable symmetry breaking for CSPs with interchangeable values. In Proceedings of IJCAI’03 (pp. 277–282). San Francisco: Morgan Kaufmann.

    Google Scholar 

  34. Van Hentenryck, P., Flener, P., Pearson, J., & Ågren, M. (2005). Compositional derivation of symmetries for constraint satisfaction. In J.-D. Zucker & L. Saitta (Eds.), Proceedings of SARA’05, LNAI (Vol. 3607, pp. 234–247). New York: Springer.

    Google Scholar 

  35. Walsh, T. (2007). Breaking value symmetry. In C. Bessière (Ed.), Proceedings of CP’07, LNCS (Vol. 4741, pp. 880–887). New York: Springer.

    Google Scholar 

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Authors and Affiliations

  1. Department of Information Technology, Uppsala University, Box 337, 751 05, Uppsala, Sweden

    Pierre Flener & Justin Pearson

  2. Department of Computer Science, Brown University, Box 1910, Providence, RI, 02912, USA

    Meinolf Sellmann & Pascal Van Hentenryck

  3. SICS, Box 1263, 164 29, Kista, Sweden

    Magnus Ågren

Authors
  1. Pierre Flener
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  2. Justin Pearson
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  3. Meinolf Sellmann
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  4. Pascal Van Hentenryck
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  5. Magnus Ågren
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Correspondence to Pierre Flener.

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The authors’ names are ordered according to the Swedish alphabet.

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Flener, P., Pearson, J., Sellmann, M. et al. Dynamic structural symmetry breaking for constraint satisfaction problems. Constraints 14, 506–538 (2009). https://doi.org/10.1007/s10601-008-9059-7

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