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A 5.875-approximation for the Traveling Tournament Problem

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  • Stephan Westphal
  • Karl Noparlik

Abstract

In this paper we propose an approximation for the Traveling Tournament Problem which is the problem of designing a schedule for a sports league consisting of a set of teams T such that the total traveling costs of the teams are minimized. It is not allowed for any team to have more than k home-games or k away-games in a row. We propose an algorithm which approximates the optimal solution by a factor of 2+2k/n+k/(n−1)+3/n+3/(2⋅k) which is not more than 5.875 for any choice of k≥4 and n≥6. This is the first constant factor approximation for k>3. We furthermore show that this algorithm is also applicable to real-world problems as it produces solutions of high quality in a very short amount of time. It was able to find solutions for a number of well known benchmark instances which are even better than the previously known ones. Copyright The Author(s) 2014

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  • Stephan Westphal & Karl Noparlik, 2014. "A 5.875-approximation for the Traveling Tournament Problem," Annals of Operations Research, Springer, vol. 218(1), pages 347-360, July.
    • Handle: RePEc:spr:annopr:v:218:y:2014:i:1:p:347-360:10.1007/s10479-012-1061-1
    DOI: 10.1007/s10479-012-1061-1
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    References listed on IDEAS

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    1. Ribeiro, Celso C. & Urrutia, Sebastian, 2007. "Heuristics for the mirrored traveling tournament problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 775-787, June.
    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. 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.
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