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An approximation algorithm for the traveling tournament problem

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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.

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References

  • Anagnostopoulos, A., Michel, L., Van Hentenryck, P., & Vergados, Y. (2006). A simulated annealing approach to the traveling tournament problem. Journal of Scheduling, 9, 177–193.

    Article  Google Scholar 

  • Easton, K., Nemhauser, G., & Trick, M. (2001). The traveling tournament problem: description and benchmarks. Lecture Notes in Computer Science, 2239, 580–585.

    Article  Google Scholar 

  • Fujiwara, N., Imahori, S., Matsui, T., & Miyashiro, R. (2007). Constructive algorithms for the constant distance traveling tournament problem. Lecture Notes in Computer Science, 3867, 135–146.

    Article  Google Scholar 

  • Haimovich, M., & Rinnooy Kan, A. H. G. (1985). Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research, 10, 527–542.

    Article  Google Scholar 

  • Hassin, R., & Rubinstein, S. (2005). On the complexity of the k-customer vehicle routing problem. Operations Research Letters, 33, 71–76.

    Article  Google Scholar 

  • Lenstra, J. K., & Rinnooy Kan, A. H. G. (1981). Complexity of vehicle routing and scheduling problems. Networks, 11, 221–227.

    Article  Google Scholar 

  • Motwani, R., & Raghavan, P. (1995). Randomized algorithms. London: Cambridge University Press.

    Google Scholar 

  • Rasmussen, R. V., & Trick, M. A. (2007). A Benders approach for the constrained minimum break problem. European Journal of Operational Research, 177, 198–213.

    Article  Google Scholar 

  • Rasmussen, R. V., & Trick, M. A. (2008). Round robin scheduling—a survey. European Journal of Operational Research, 188, 617–636.

    Article  Google Scholar 

  • Trick, M. (1999). Challenge traveling tournament problems. http://mat.gsia.cmu.edu/TOURN/. Accessed 16 July 2009.

  • Van Hentenryck, P., & Vergados, Y. (2006). Traveling tournament scheduling: a systematic evaluation of simulated annealling. Lecture Notes in Computer Science, 3990, 228–243.

    Article  Google Scholar 

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Author notes

  1. Shinji Imahori

    Present address: Graduate School of Engineering, Nagoya University, Nagoya, Japan

Authors and Affiliations

  1. Institute of Engineering, Tokyo University of Agriculture and Technology, Naka-cho, Koganei-shi, Tokyo, 184-8588, Japan

    Ryuhei Miyashiro

  2. Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Tomomi Matsui

  3. Graduate School of Information Science and Technology, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Shinji Imahori

Authors
  1. Ryuhei Miyashiro
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  2. Tomomi Matsui
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  3. Shinji Imahori
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Corresponding author

Correspondence to Ryuhei Miyashiro.

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Miyashiro, R., Matsui, T. & Imahori, S. An approximation algorithm for the traveling tournament problem. Ann Oper Res 194, 317–324 (2012). https://doi.org/10.1007/s10479-010-0742-x

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  • DOI: https://doi.org/10.1007/s10479-010-0742-x

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