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An approximation algorithm for the traveling tournament problem

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  • Ryuhei Miyashiro
  • Tomomi Matsui
  • Shinji Imahori

Abstract

This paper describes the traveling tournament problem, a well-known benchmark problem in the field of tournament timetabling. We propose a new lower bound for the traveling tournament problem, and construct a randomized approximation algorithm yielding a feasible solution whose approximation ratio is less than 2+(9/4)/(n−1), where n is the number of teams. Additionally, we propose a deterministic approximation algorithm with the same approximation ratio using a derandomization technique. For the traveling tournament problem, the proposed algorithms are the first approximation algorithms with a constant approximation ratio, which is less than 2+3/4. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Ryuhei Miyashiro & Tomomi Matsui & Shinji Imahori, 2012. "An approximation algorithm for the traveling tournament problem," Annals of Operations Research, Springer, vol. 194(1), pages 317-324, April.
    • Handle: RePEc:spr:annopr:v:194:y:2012:i:1:p:317-324:10.1007/s10479-010-0742-x
    DOI: 10.1007/s10479-010-0742-x
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    1. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    2. 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.
    3. Rasmussen, Rasmus V. & Trick, Michael A., 2007. "A Benders approach for the constrained minimum break problem," European Journal of Operational Research, Elsevier, vol. 177(1), pages 198-213, February.
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    Cited by:

    1. Clemens Thielen & Stephan Westphal, 2012. "Approximation algorithms for TTP(2)," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 1-20, August.
    2. Richard Hoshino & Ken-ichi Kawarabayashi, 2013. "An Approximation Algorithm for the Bipartite Traveling Tournament Problem," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 720-728, November.
    3. Bender Marco & Westphal Stephan, 2016. "A combined approximation for the traveling tournament problem and the traveling umpire problem," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(3), pages 139-149, September.
    4. Shinji Imahori & Tomomi Matsui & Ryuhei Miyashiro, 2014. "A 2.75-approximation algorithm for the unconstrained traveling tournament problem," Annals of Operations Research, Springer, vol. 218(1), pages 237-247, July.

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