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A 5-approximation algorithm for the traveling tournament problem

Author

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  • Jingyang Zhao

    (University of Electronic Science and Technology of China)

  • Mingyu Xiao

    (University of Electronic Science and Technology of China)

Abstract

The Traveling Tournament Problem (TTP-k) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all n teams is minimized under the constraints that each pair of teams plays one game in each other’s home venue, and each team plays at most k-consecutive home games or away games. Westphal and Noparlik (Ann. Oper. Res. 218(1):347-360, 2014) claimed a 5.875-approximation algorithm for all $$k\ge 4$$ k ≥ 4 and $$n\ge 6$$ n ≥ 6 . However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a 5-approximation algorithm for all k and n. Furthermore, if $$k \ge n/2$$ k ≥ n / 2 , the approximation ratio can be improved to 4.

Suggested Citation

  • Jingyang Zhao & Mingyu Xiao, 2025. "A 5-approximation algorithm for the traveling tournament problem," Annals of Operations Research, Springer, vol. 346(3), pages 2287-2305, March.
    • Handle: RePEc:spr:annopr:v:346:y:2025:i:3:d:10.1007_s10479-025-06483-1
    DOI: 10.1007/s10479-025-06483-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Marc Goerigk & Stephan Westphal, 2016. "A combined local search and integer programming approach to the traveling tournament problem," Annals of Operations Research, Springer, vol. 239(1), pages 343-354, April.
    4. Lim, A. & Rodrigues, B. & Zhang, X., 2006. "A simulated annealing and hill-climbing algorithm for the traveling tournament problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1459-1478, November.
    5. Van Bulck, David & Goossens, Dries & Schönberger, Jörn & Guajardo, Mario, 2020. "RobinX: A three-field classification and unified data format for round-robin sports timetabling," European Journal of Operational Research, Elsevier, vol. 280(2), pages 568-580.
    6. 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.
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