Skip to main content
SpringerLink
Log in

Characterizing Feasible Pattern Sets with a Minimum Number of Breaks

  • Conference paper
Practice and Theory of Automated Timetabling IV (PATAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2740))

Abstract

In sports timetabling, creating an appropriate timetable for a round-robin tournament with home–away assignment is a significant problem. To solve this problem, we need to construct home–away assignment that can be completed into a timetable; such assignment is called a feasible pattern set. Although finding feasible pattern sets is at the heart of many timetabling algorithms, good characterization of feasible pattern sets is not known yet. In this paper, we consider the feasibility of pattern sets, and propose a new necessary condition for feasible pattern sets. In the case of a pattern set with a minimum number of breaks, we prove a theorem leading a polynomial-time algorithm to check whether a given pattern set satisfies the necessary condition. Computational experiment shows that, when the number of teams is less than or equal to 26, the proposed condition characterizes feasible pattern sets with a minimum number of breaks.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armstrong, J.R., Willis, R.J.: Scheduling the Cricket World Cup – a Case Study. J. Oper. Res. Soc. 44, 1067–1072 (1993)

    MATH  Google Scholar 

  2. Blest, D.C., Fitzgerald, D.G.: Scheduling Sports Competitions with a Given Distribution of Times. Discr. Appl. Math. 22, 9–19 (1989)

    Article  MathSciNet  Google Scholar 

  3. de Werra, D.: Geography, Games and Graphs. Discr. Appl. Math. 2, 327–337 (1980)

    Article  MATH  Google Scholar 

  4. de Werra, D.: Minimizing Irregularities in Sports Schedules Using Graph Theory. Discr. Appl. Math. 4, 217–226 (1982)

    Article  MATH  Google Scholar 

  5. de Werra, D.: On the Multiplication of Divisions: the Use of Graphs for Sports Scheduling. Networks 15, 125–136 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  6. de Werra, D.: Some Models of Graphs for Scheduling Sports Competitions. Discr. Appl. Math. 21, 47–65 (1988)

    Article  MATH  Google Scholar 

  7. Ferland, J.A., Fleurent, C.: Computer Aided Scheduling for a Sport League. INFOR 29, 14–25 (1991)

    Google Scholar 

  8. Henz, M.: Scheduling a Major College Basketball Conference—Revisited. Oper. Res. 49, 163–168 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. ILOG: ILOG CPLEX 7.0 User’s Manual. ILOG, Gentilly (2000)

    Google Scholar 

  10. Miyashiro, R., Matsui, T.: Note on Equitable Round-Robin Tournaments. In: Proc. 6th KOREA–JAPAN Joint Workshop on Algorithms and Computation, pp. 135–140 (2001)

    Google Scholar 

  11. Miyashiro, R., Matsui, T.: Notes on Equitable Round-Robin Tournaments. IEICE Trans. Fund. Electron. Commun. Comput. Sci. E85-A, 1006–1010 (2002)

    Google Scholar 

  12. Nemhauser, G.L., Trick, M.A.: Scheduling a Major College Basketball Conference. Oper. Res. 46, 1–8 (1998)

    Article  Google Scholar 

  13. Russell, K.G.: Balancing Carry-Over Effects in Round Robin Tournaments. Biometrika 67, 127–131 (1980)

    Article  MathSciNet  Google Scholar 

  14. Russell, R.A., Leung, J.M.Y.: Devising a Cost Effective Schedule for a Baseball League. Oper. Res. 42, 614–625 (1994)

    Article  MATH  Google Scholar 

  15. Schreuder, J.A.M.: Combinatorial Aspects of Construction of Competition Dutch Professional Football Leagues. Discr. Appl. Math. 35, 301–312 (1992)

    Article  MATH  Google Scholar 

  16. Trick, M.A.: A Scheduling-Then-Break Approach to Sports Timetabling. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 242–253. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. van Weert, A., Schreuder, J.A.M.: Construction of Basic Match Schedules for Sports Competitions by Using Graph Theory. In: Burke, E.K., Carter, M. (eds.) PATAT 1997. LNCS, vol. 1408, pp. 201–210. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Willis, R.J., Terrill, B.J.: Scheduling the Australian State Cricket Season Using Simulated Annealing. J. Oper. Res. Soc. 45, 276–280 (1994)

    MATH  Google Scholar 

  19. Wright, M.: Timetabling County Cricket Fixtures Using a Form of Tabu Search. J. Oper. Res. Soc. 45, 758–770 (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan

    Ryuhei Miyashiro & Tomomi Matsui

  2. Department of Computer Science, The University of Electro-Communications, Tokyo, 182-8585, Japan

    Hideya Iwasaki

Authors
  1. Ryuhei Miyashiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hideya Iwasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomomi Matsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund Burke

  2. Information Technology, KaHo St-Lieven, Gebr. Desmetstraat 1, 9000, Gent, Belgium

    Patrick De Causmaecker

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Miyashiro, R., Iwasaki, H., Matsui, T. (2003). Characterizing Feasible Pattern Sets with a Minimum Number of Breaks. In: Burke, E., De Causmaecker, P. (eds) Practice and Theory of Automated Timetabling IV. PATAT 2002. Lecture Notes in Computer Science, vol 2740. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45157-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45157-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40699-0

  • Online ISBN: 978-3-540-45157-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation