Skip to main content
Springer Nature Link
Log in

A Further Improvement on Approximating TTP-2

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

Included in the following conference series:

  • 1302 Accesses

Abstract

The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other’s home venue, minimizing the total distance traveled by all n teams (n is even). In this paper, we consider TTP-2, i.e., TTP with one more constraint that each team can have at most two consecutive home games or away games. Due to the different structural properties, known algorithms for TTP-2 are different for n/2 being odd and even. For odd n/2, the best known approximation ratio is about \((1+12/n)\), and for even n/2, the best known approximation ratio is about \((1+4/n)\). In this paper, we further improve the approximation ratio from \((1+4/n)\) to \((1+3/n)\) for n/2 being even. Experimental results on benchmark sets show that our algorithm can improve previous results on all instances with even n/2 by \(1\%\) to \(4\%\).

The work is supported by the National Natural Science Foundation of China, under grant 61972070.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Anagnostopoulos, A., Michel, L., Van Hentenryck, P., Vergados, Y.: A simulated annealing approach to the traveling tournament problem. J. Sched. 9(2), 177–193 (2006)

    Article  Google Scholar 

  2. Bhattacharyya, R.: Complexity of the unconstrained traveling tournament problem. Oper. Res. Lett. 44(5), 649–654 (2016)

    Article  MathSciNet  Google Scholar 

  3. Campbell, R.T., Chen, D.: A minimum distance basketball scheduling problem. Manage. Sci. Sports 4, 15–26 (1976)

    MATH  Google Scholar 

  4. Di Gaspero, L., Schaerf, A.: A composite-neighborhood tabu search approach to the traveling tournament problem. J. Heurist. 13(2), 189–207 (2007)

    Article  Google Scholar 

  5. Easton, K., Nemhauser, G., Trick, M.: The traveling tournament problem description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–584. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45578-7_43

    Chapter  MATH  Google Scholar 

  6. Easton, K., Nemhauser, G., Trick, M.: Solving the travelling tournament problem: a combined integer programming and constraint programming approach. In: Burke, E., De Causmaecker, P. (eds.) PATAT 2002. LNCS, vol. 2740, pp. 100–109. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45157-0_6

    Chapter  Google Scholar 

  7. Goerigk, M., Hoshino, R., Kawarabayashi, K., Westphal, S.: Solving the traveling tournament problem by packing three-vertex paths. In: AAAI 2014, pp. 2271–2277 (2014)

    Google Scholar 

  8. Hoshino, R., Kawarabayashi, K.I.: An approximation algorithm for the bipartite traveling tournament problem. Math. Oper. Res. 38(4), 720–728 (2013)

    Article  MathSciNet  Google Scholar 

  9. Imahori, S., Matsui, T., Miyashiro, R.: A 2.75-approximation algorithm for the unconstrained traveling tournament problem. Ann. Oper. Res. 218(1), 237–247 (2012). https://doi.org/10.1007/s10479-012-1161-y

    Article  MathSciNet  MATH  Google Scholar 

  10. Kendall, G., Knust, S., Ribeiro, C.C., Urrutia, S.: Scheduling in sports: an annotated bibliography. Comput. Oper. Res. 37(1), 1–19 (2010)

    Article  MathSciNet  Google Scholar 

  11. Lim, A., Rodrigues, B., Zhang, X.: A simulated annealing and hill-climbing algorithm for the traveling tournament problem. Eur. J. Oper. Res. 174(3), 1459–1478 (2006)

    Article  MathSciNet  Google Scholar 

  12. Miyashiro, R., Matsui, T., Imahori, S.: An approximation algorithm for the traveling tournament problem. Ann. Oper. Res. 194(1), 317–324 (2012)

    Article  MathSciNet  Google Scholar 

  13. Rasmussen, R.V., Trick, M.A.: Round robin scheduling-a survey. Eur. J. Oper. Res. 188(3), 617–636 (2008)

    Article  MathSciNet  Google Scholar 

  14. Thielen, C., Westphal, S.: Complexity of the traveling tournament problem. Theoret. Comput. Sci. 412(4), 345–351 (2011)

    Article  MathSciNet  Google Scholar 

  15. Thielen, C., Westphal, S.: Approximation algorithms for TTP(2). Math. Methods Oper. Res. 76(1), 1–20 (2012)

    Article  MathSciNet  Google Scholar 

  16. Trick, M.: Challenge traveling tournament instances (2013). http://mat.gsia.cmu.edu/TOURN/

  17. de Werra, D.: Some models of graphs for scheduling sports competitions. Discret. Appl. Math. 21(1), 47–65 (1988)

    Article  MathSciNet  Google Scholar 

  18. Westphal, S., Noparlik, K.: A 5.875-approximation for the traveling tournament problem. Ann. Oper. Res. 218(1), 347–360 (2014)

    Article  MathSciNet  Google Scholar 

  19. Xiao, M., Kou, S.: An improved approximation algorithm for the traveling tournament problem with maximum trip length two. In: MFCS 2016, pp. 89:1–89:14 (2016)

    Google Scholar 

  20. Yamaguchi, D., Imahori, S., Miyashiro, R., Matsui, T.: An improved approximation algorithm for the traveling tournament problem. Algorithmica 61(4), 1077–1091 (2011)

    Article  MathSciNet  Google Scholar 

  21. Zhao, J., Xiao, M.: A further improvement on approximating TTP-2. CoRR abs/2108.13060 (2021)

    Google Scholar 

  22. Zhao, J., Xiao, M.: The traveling tournament problem with maximum tour length two: a practical algorithm with an improved approximation bound. In: IJCAI 2021, pp. 4206–4212 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Jingyang Zhao & Mingyu Xiao

Authors
  1. Jingyang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mingyu Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhao, J., Xiao, M. (2021). A Further Improvement on Approximating TTP-2. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-89543-3_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics