Annals of Operations Research

, Volume 194, Issue 1, pp 427–438 | Cite as

An improved SAT formulation for the social golfer problem

  • Markus TriskaEmail author
  • Nysret Musliu


The Social Golfer Problem (SGP) is a sports scheduling problem that exhibits a lot of symmetry and has recently attracted significant attention. In this paper, we first revisit an existing SAT encoding for the SGP and correct some of its clauses. We then propose a change in the encoding that significantly reduces the number of variables for all instances. We achieve considerable performance improvements when solving many SGP instances with common SAT solvers using local search and complete backtracking. This makes SAT formulations a more promising approach for solving the SGP than previously.


Sports scheduling Combinatorial optimization Design theory Finite geometry 


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  1. Anderson, I. (1997). Combinatorial designs and tournaments. Oxford: Clarendon. Google Scholar
  2. Barnier, N., & Brisset, P. (2005). Solving Kirkman’s schoolgirl problem in a few seconds. Constraints, 10(1), 7–21. CrossRefGoogle Scholar
  3. Colbourn, C. J. (1984). The complexity of completing partial Latin squares. Discrete Applied Mathematics, 8, 25–30. CrossRefGoogle Scholar
  4. Colbourn, C. H., & Dinitz, J. H. (1996). The CRC handbook of combinatorial designs. Boca Raton: CRC Press. CrossRefGoogle Scholar
  5. Cotta, C., Dotú, I., Fernández, A. J., & Hentenryck, P. V. (2006). Scheduling social golfers with memetic evolutionary programming. In LNCS : Vol. 4030. Hybrid metaheuristics (pp. 150–161). Berlin: Springer. CrossRefGoogle Scholar
  6. Crawford, J. M., Ginsberg, M. L., Luks, E. M., & Roy, A. (1996). Symmetry-breaking predicates for search problems. In KR (pp. 148–159). Google Scholar
  7. Dotú, I., & Hentenryck, P. V. (2005). Scheduling social golfers locally. In LNCS : Vol. 3524. CPAIOR (pp. 155–167). Berlin: Springer. Google Scholar
  8. Flener, P., Frisch, A. M., Hnich, B., Kiziltan, Z., Miguel, I., Pearson, J., & Walsh, T. (2002). Breaking row and column symmetries in matrix models. In LNCS : Vol. 2470. CP’02. Berlin: Springer. Google Scholar
  9. Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., & Walsh, T. (2002). Global constraints for lexicographic orderings. In LNCS : Vol. 2470. CP’02. Berlin: Springer. Google Scholar
  10. Gent, I., & Lynce, I. (2005). A SAT encoding for the social golfer problem. In IJCAI’05 workshop on modelling and solving problems with constraints. Google Scholar
  11. Gent, I. P., & Walsh, T. (1999). CSPLib: a benchmark library for constraints. In LNCS : Vol. 1713. CP’99. Berlin: Springer. Google Scholar
  12. Harvey, W., & Winterer, T. (2005). Solving the MOLR and social golfers problems. In LNCS : Vol. 3709. CP’05 (pp. 286–300). Berlin: Springer. Google Scholar
  13. Petrie, K. E., & Smith, B. (2004). Dynamic symmetry breaking in constraint programming and linear programming (Technical report). Google Scholar
  14. Prestwich, S. (2001). First-solution search with symmetry breaking and implied constraints. In Proceedings of the CP’01 workshop on modelling and problem formulation. Google Scholar
  15. Selman, B., Kautz, H., & Cohen, B. (1993). Local search strategies for satisfiability testing. In Second DIMACS implementation challenge. Google Scholar
  16. Zhang, H. (1997). SATO: an efficient propositional prover. In LNAI : Vol. 1249. CADE. Berlin: Springer. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Database and Artificial Intelligence GroupVienna University of TechnologyViennaAustria

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