Sports tournaments, home-away assignments, and the break minimization problem

Gerhard F. Post, Gerhard Woeginger

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Abstract

We consider the break minimization problem for fixing home-away assignments in round-robin sports tournaments. First, we show that for an opponent schedule with $n$ teams and $n-1$ rounds, there always exists a home-away assignment with at most $\frac14 n(n-2)$ breaks. Secondly, for infinitely many $n$, we construct opponent schedules for which at least $\frac16 n(n-1)$ breaks are necessary. Finally, we prove that break minimization for $n$ teams and a partial opponent schedule with $r$ rounds is an NP-hard problem for $r\ge3$. This is in strong contrast to the case of $r=2$ rounds, which can be scheduled (in polynomial time) without any breaks.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages14
ISBN (Print)0169-2690
Publication statusPublished - 2005

Publication series

NameMemorandum Afdeling TW
PublisherDepartment of Applied Mathematics, University of Twente
No.1760
ISSN (Print)0169-2690

Keywords

  • MSC-90B35
  • METIS-225439
  • IR-65944
  • EWI-3580

Cite this

Post, G. F., & Woeginger, G. (2005). Sports tournaments, home-away assignments, and the break minimization problem. (Memorandum Afdeling TW; No. 1760). Enschede: University of Twente.