Sports League Scheduling: Enumerative Search for Prob026 from CSPLib

  • Jean-Philippe Hamiez
  • Jin-Kao Hao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4204)


This paper presents an enumerative approach for a sports league scheduling problem. This simple method can solve some instances involving a number T of teams up to 70 while the best known constraint programing algorithm is limited to T≤40. The proposed approach relies on interesting properties which are used to constraint the search process.


Constraint Programming Constraint Satisfaction Problem Combinatorial Design Constraint Reasoning Constraint Programming Approach 
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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  1. 1.
    Gent, I., Walsh, T.: CSPLib: A benchmark library for constraints. . In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 480–481. Springer, Heidelberg (1998), Google Scholar
  2. 2.
    Colbourn, C., Dinitz, J. (eds.): The CRC Handbook of Combinatorial Designs. Discrete Mathematics and Its Applications, vol. 4. CRC Press, Boca Raton (1996)MATHGoogle Scholar
  3. 3.
    Gelling, E., Odeh, R.: On 1-factorizations of the complete graph and the relationship to round-robin schedules. Congressus Numerantium 9, 213–221 (1974)MathSciNetGoogle Scholar
  4. 4.
    McAloon, K., Tretkoff, C., Wetzel, G.: Sports league scheduling. In: Proceedings of the Third ILOG Optimization Suite International Users’ Conference (1997)Google Scholar
  5. 5.
    Gomes, C., Selman, B., McAloon, K., Tretkoff, C.: Randomization in backtrack search: Exploiting heavy-tailed profiles for solving hard scheduling problems. In: Proceedings AIPS 1998, pp. 208–213. AAAI Press, Menlo Park (1998)Google Scholar
  6. 6.
    Béjar, R., Manyà, F.: Solving combinatorial problems with regular local search algorithms. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS (LNAI), vol. 1705, pp. 33–43. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Gomes, C., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: Proceedings AAAI/IAAI 1998, pp. 431–437. AAAI Press/MIT Press (1998)Google Scholar
  8. 8.
    Béjar, R., Manyà, F.: Solving the round robin problem using propositional logic. In: Proceedings AAAI/IAAI 2000, pp. 262–266. AAAI Press/MIT Press (2000)Google Scholar
  9. 9.
    Régin, J.-C.: Modeling and solving sports league scheduling with constraint programming. In: Proceedings INFORMS 1998 (1998)Google Scholar
  10. 10.
    Wetzel, G., Zabatta, F.: Technical report, City University of New York, USA (1998)Google Scholar
  11. 11.
    Van Hentenryck, P., et al.: Constraint programming in OPL. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 98–116. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Régin, J.-C.: Constraint programming and sports scheduling problems. In: Proceedings INFORMS 1999 (1999)Google Scholar
  13. 13.
    Hamiez, J.-P., Hao, J.-K.: Solving the sports league scheduling problem with tabu search. In: Nareyek, A. (ed.) ECAI-WS 2000. LNCS, vol. 2148, pp. 24–36. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Schellenberg, P., van Rees, G., Vanstone, S.: The existence of balanced tournament designs. Ars Combinatoria 3, 303–318 (1977)MATHMathSciNetGoogle Scholar
  15. 15.
    Hamiez, J.P., Hao, J.K.: A linear-time algorithm to solve the Sports League Scheduling Problem (prob026 of CSPLib). Discrete Applied Mathematics 143, 252–265 (2004)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Haselgrove, J., Leech, J.: A tournament design problem. American Mathematical Monthly 84(3), 198–201 (1977)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Gomes, C.P., Sellmann, M.: Streamlined constraint reasoning. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 274–289. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Lockwood, E.H.: American tournaments. The Mathematical Gazette 20, 333 (1936)CrossRefGoogle Scholar
  19. 19.
    Flener, P., Frisch, A.M., 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Philippe Hamiez
    • 1
  • Jin-Kao Hao
    • 1
  1. 1.LERIAUniversité d’Angers, UFR SciencesAngersFrance

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