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An Improved Approximation Algorithm for the Traveling Tournament Problem

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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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 an approximation algorithm for the traveling tournament problem with the constraints such that both the number of consecutive away games and that of consecutive home games are at most k. When k ≤ 5, the approximation ratio of the proposed algorithm is bounded by (2k − 1)/k + O(k/n) where n denotes the number of teams; when k > 5, the ratio is bounded by (5k − 7)/(2k) + O(k/n). For k = 3, the most investigated case of the traveling tournament problem to date, the approximation ratio of the proposed algorithm is 5/3 + O(1/n); this is better than the previous approximation algorithm proposed for k = 3, whose approximation ratio is 2 + O(1/n).

This is an extended abstract. Proofs of theorems and lemmas are omitted due to page limitation. They are available in our technical report [7].

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References

  1. Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem. Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University (1976)

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  2. Easton, K., Nemhauser, G., Trick, M.: The traveling tournament problem: description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–585. Springer, Heidelberg (2001)

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  3. Miyashiro, R., Matsui, T., Imahori, S.: An approximation algorithm for the traveling tournament problem. In: The 7th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2008), Université de Montréal, CD-ROM (2008)

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  6. Trick, M.: Challenge traveling tournament problems (2009), http://mat.gsia.cmu.edu/TOURN/

  7. Yamaguchi, D., Imahori, S., Miyashiro, R., Matsui, T.: An improved approximation algorithm for the traveling tournament problem, Mathematical Engineering Technical Report, METR09-42, Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo

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Author information

Authors and Affiliations

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

    Daisuke Yamaguchi & Tomomi Matsui

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

    Shinji Imahori

  3. Institute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology, Naka-cho, Koganei, Tokyo, 184-8588, Japan

    Ryuhei Miyashiro

Authors
  1. Daisuke Yamaguchi
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  2. Shinji Imahori
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  3. Ryuhei Miyashiro
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  4. Tomomi Matsui
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Yamaguchi, D., Imahori, S., Miyashiro, R., Matsui, T. (2009). An Improved Approximation Algorithm for the Traveling Tournament Problem. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_69

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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