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Evaluation of Length-Lex Set Variables

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5732))

Abstract

This paper presents the first experimental evaluation of the length-lex domain for set variables. The implementation is based on bound-consistency algorithms proposed in earlier work and two novel technical contributions: a generic filtering algorithm which automatically pushes ordering constraints into symmetric binary constraints with only a logarithmic overhead and an adaptation of symmetry-breaking constraints from 0/1 matrices to the length-lex ordering. The experimental results indicate that the length-lex representation for set variables is very effective and robust on traditional set-CSPs benchmarks.

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References

  1. Puget, J.F.: Pecos a high level constraint programming language. In: Proc. of Spicis (1992)

    Google Scholar 

  2. Gervet, C.: Interval propagation to reason about sets: Definition and implementation of a practical language. Constraints 1(3), 191–244 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Azevedo, F., Barahona, P.: Modelling digital circuits problems with set constraints. In: CP 2000, pp. 414–428 (2000)

    Google Scholar 

  4. Azevedo, F.: Cardinal: A finite sets constraint solver. Constraints 12(1), 93–129 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sadler, A., Gervet, C.: Hybrid set domains to strengthen constraint propagation and reduce symmetries. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 604–618. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Sadler, A., Gervet, C.: Enhancing set constraint solvers with lexicographic bounds. J. Heuristics 14(1), 23–67 (2008)

    Article  MATH  Google Scholar 

  7. Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Pearson, J., Walsh, T.: Breaking row and column symmetries in matrix models. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 462–476. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Frisch, A.M., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Propagation algorithms for lexicographic ordering constraints. Artificial Intelligence (170) (2006)

    Google Scholar 

  9. Peter Hawkins, V.L., Stuckey, P.J.: Solving set constraint satisfaction problems using robdds. JAIR 24, 109–156 (2005)

    MATH  Google Scholar 

  10. Gervet, C., Van Hentenryck, P.: Length-lex ordering for set csps. In: AAAI 2006 (2006)

    Google Scholar 

  11. Hnich, B., Kiziltan, Z., Walsh, T.: Combining symmetry breaking with other constraints: Lexicographic ordering with sums. In: AMAI 2004 (2004)

    Google Scholar 

  12. Cheng, B.M.W., Choi, K.M.F., Lee, J.H.M., Wu, J.C.K.: Increasing constraint propagation by redundant modeling: an experience report. Constraints 4(2), 167–192 (1999)

    Article  MATH  Google Scholar 

  13. Geelen, P.A.: Dual viewpoint heuristics for binary constraint satisfaction problems. In: ECAI 1992, pp. 31–35 (1992)

    Google Scholar 

  14. Law, Y.C., Lee, J.H.M.: Symmetry breaking constraints for value symmetries in constraint satisfaction. Constraints 11 (2006)

    Google Scholar 

  15. Puget, J.F.: An efficient way of breaking value symmetries. In: AAAI 2006 (2006)

    Google Scholar 

  16. Walsh, T.: General symmetry breaking constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 650–664. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Van Hentenryck, P., Yip, J., Gervet, C., Dooms, G.: Bound consistency for binary length-lex set constraints. In: AAAI 2008, pp. 375–380 (2008)

    Google Scholar 

  18. Yip, J., Van Hentenryck, P.: Length-lex bound consistency for knapsack constraints. In: SAC 2009 (2009)

    Google Scholar 

  19. Malitsky, Y., Sellmann, M., van Hoeve, W.J.: Length-lex bounds consistency for knapsack constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 266–281. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Katsirelos, G., Narodytska, N., Walsh, T.: Combining symmetry breaking and global constraints. In: CSCLP 2008 (2009)

    Google Scholar 

  21. van Hoeve, W.J., Sabharwal, A.: Filtering atmost1 on pairs of set variables. In: Perron, L., Trick, M.A. (eds.) CPAIOR 2008. LNCS, vol. 5015, pp. 382–386. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Kiziltan, Z.: Symmetry breaking ordering constraints. Phd Thesis. Uppsala University

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Yip, J., Van Hentenryck, P. (2009). Evaluation of Length-Lex Set Variables. In: Gent, I.P. (eds) Principles and Practice of Constraint Programming - CP 2009. CP 2009. Lecture Notes in Computer Science, vol 5732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_63

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  • DOI: https://doi.org/10.1007/978-3-642-04244-7_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04243-0

  • Online ISBN: 978-3-642-04244-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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