Characterizing Feasible Pattern Sets with a Minimum Number of Breaks

  • Ryuhei Miyashiro
  • Hideya Iwasaki
  • Tomomi Matsui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2740)


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.


Computational Experiment Integer Programming Problem Black Vertex Partial Assignment Complement Pair 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ryuhei Miyashiro
    • 1
  • Hideya Iwasaki
    • 2
  • Tomomi Matsui
    • 1
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan
  2. 2.Department of Computer ScienceThe University of Electro-CommunicationsTokyoJapan

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