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A greedy algorithm for the social golfer and the Oberwolfach problem

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  • Schmand, Daniel
  • Schröder, Marc
  • Vargas Koch, Laura

Abstract

Inspired by the increasing popularity of Swiss-system tournaments in sports, we study the problem of predetermining the number of rounds that can be guaranteed in a Swiss-system tournament. Matches of these tournaments are usually determined in a myopic round-based way dependent on the results of previous rounds. Together with the hard constraint that no two players meet more than once during the tournament, at some point it might become infeasible to schedule a next round. For tournaments with n players and match sizes of k≥2 players, we prove that we can always guarantee ⌊nk(k−1)⌋ rounds. We show that this bound is tight. This provides a simple polynomial time constant factor approximation algorithm for the social golfer problem.

Suggested Citation

  • Schmand, Daniel & Schröder, Marc & Vargas Koch, Laura, 2022. "A greedy algorithm for the social golfer and the Oberwolfach problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 310-319.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:1:p:310-319
    DOI: 10.1016/j.ejor.2021.09.018
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    References listed on IDEAS

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    1. Markus Triska & Nysret Musliu, 2012. "An effective greedy heuristic for the Social Golfer Problem," Annals of Operations Research, Springer, vol. 194(1), pages 413-425, April.
    2. Markus Triska & Nysret Musliu, 2012. "An improved SAT formulation for the social golfer problem," Annals of Operations Research, Springer, vol. 194(1), pages 427-438, April.
    3. Rasmussen, Rasmus V. & Trick, Michael A., 2008. "Round robin scheduling - a survey," European Journal of Operational Research, Elsevier, vol. 188(3), pages 617-636, August.
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