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

Gerhard F. Post, Gerhard Woeginger

Research output: Book/ReportReportProfessional

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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.
Post, Gerhard F. ; Woeginger, Gerhard. / Sports tournaments, home-away assignments, and the break minimization problem. Enschede : University of Twente, 2005. 14 p. (Memorandum Afdeling TW; 1760).
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note = "Imported from MEMORANDA",
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Post, GF & Woeginger, G 2005, Sports tournaments, home-away assignments, and the break minimization problem. Memorandum Afdeling TW, no. 1760, University of Twente, Enschede.

Sports tournaments, home-away assignments, and the break minimization problem. / Post, Gerhard F.; Woeginger, Gerhard.

Enschede : University of Twente, 2005. 14 p. (Memorandum Afdeling TW; No. 1760).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Sports tournaments, home-away assignments, and the break minimization problem

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AU - Woeginger, Gerhard

N1 - Imported from MEMORANDA

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - MSC-90B35

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KW - IR-65944

KW - EWI-3580

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Post GF, Woeginger G. Sports tournaments, home-away assignments, and the break minimization problem. Enschede: University of Twente, 2005. 14 p. (Memorandum Afdeling TW; 1760).