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Solving the MOLR and Social Golfers Problems

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3709)

Abstract

We present a range of techniques for tackling the problem of finding sets of Mutually Orthogonal Latin Rectangles (MOLR). In particular, we use a construction that allows us to search for solutions of a particular form with much reduced effort, and a seeding heuristic for the MOLR problem that allows a local search approach to find much better solutions than would be possible otherwise. Finally, we use the MOLR solutions found to construct solutions to the social golfer problem that improve the best known number of rounds for 43 instances, by as many as 10 rounds.

Keywords

  • Local Search
  • Constraint Programming
  • LDPC Code
  • Local Search Algorithm
  • Combinatorial Design

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Barnier, N., Brisset, P.: Solving the Kirkman’s Schoolgirl Problem in a few seconds. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 477–491. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  2. Colbourn, C.H., Dinitz, J.H. (eds.): The CRC Handbook of Combinatorial Designs. CRC Press, Rockville (1996)

    MATH  Google Scholar 

  3. Djordjevic, I.B., Vasic, B.: LDPC codes for long haul optical communications based on high-girth designs. Journal of Optical Communications 24(3), 94–96 (2003)

    Google Scholar 

  4. Dotú, I., Van Hentenryck, P.: Scheduling social golfers locally. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 155–167. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  5. Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  6. Franklin, M.F.: Triples of almost orthogonal 10 ×10 latin squares useful in experimental design. Ars Combinatoria 17, 141–146 (1984)

    MATH  MathSciNet  Google Scholar 

  7. The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.3 (2002), http://www.gap-system.org

  8. 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)

    CrossRef  Google Scholar 

  9. Gent, I.P., Walsh, T., Selman, B.: CSPLib: a problem library for constraints, http://csplib.org/

  10. Harvey, W.: Warwick’s results page for the MOLR problem, http://www.icparc.ic.ac.uk/~wh/molr

  11. Harvey, W.: Warwick’s results page for the social golfer problem, http://www.icparc.ic.ac.uk/~wh/golf

  12. Harvey, W.: Symmetry breaking and the social golfer problem. In: Flener, P., Pearson, J. (eds.) Proc. SymCon 2001: Symmetry in Constraints, pp. 9–16 (2001)

    Google Scholar 

  13. mathtalk-ga. Answer to Unique combinations of 4 numbers between 1 to N. Google Answers (2005), http://answers.google.com/answers/threadview?id=274891

  14. Michel, L., Van Hentenryck, P.: A simple tabu search for warehouse location. European Journal of Operations Research 157(3), 576–591 (2004)

    MATH  CrossRef  Google Scholar 

  15. Mullen, G.L., Shiue, J.-S.: A simple construction for orthogonal latin rectangles. Journal of Combinatorial Mathematics and Combinatorial Computing 9, 161–166 (1991)

    MATH  MathSciNet  Google Scholar 

  16. Prestwich, S.: Randomised backtracking for linear pseudo-boolean constraint problems. In: Jussien, N., Laburthe, F. (eds.) Proc. of the Fourth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR 2002), Le Croisic, France, March, 25–27, pp. 7–19 (2002)

    Google Scholar 

  17. Puget, J.-F.: Symmetry breaking revisited. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 446–461. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  18. Sharma, V.K., Das, M.N.: On resolvable incomplete block designs. Austral. J. Statist. 27(3), 298–302 (1985)

    MATH  CrossRef  MathSciNet  Google Scholar 

  19. Smith, B.M.: Reducing symmetry in a combinatorial design problem. In: CPAIOR 2001: Proc. of the Third International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, April 2001, pp. 351–359 (2001)

    Google Scholar 

  20. Stinson, D.R., Wei, R., Zhu, L.: New constructions for perfect hash families and related structures using combinatorial designs and codes. Journal of Combinatorial Designs 8(3), 189–200 (2000)

    MATH  CrossRef  MathSciNet  Google Scholar 

  21. Wallace, M.G., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12(1), 159–200 (1997)

    Google Scholar 

  22. Wanless, I.M.: Answers to questions by Dénes on latin power sets. Europ. J. Combinatorics 22, 1009–1020 (2001)

    MATH  CrossRef  MathSciNet  Google Scholar 

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Harvey, W., Winterer, T. (2005). Solving the MOLR and Social Golfers Problems. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_23

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  • DOI: https://doi.org/10.1007/11564751_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29238-8

  • Online ISBN: 978-3-540-32050-0

  • eBook Packages: Computer ScienceComputer Science (R0)