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

Gerhard F. Post, Gerhard Woeginger

Research output: Book/ReportReportProfessional

### 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 language Undefined Enschede University of Twente 14 0169-2690 Published - 2005

### Publication series

Name Memorandum Afdeling TW Department of Applied Mathematics, University of Twente 1760 0169-2690

• 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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title = "Sports tournaments, home-away assignments, and the break minimization problem",
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.",
keywords = "MSC-90B35, METIS-225439, IR-65944, EWI-3580",
author = "Post, {Gerhard F.} and Gerhard Woeginger",
note = "Imported from MEMORANDA",
year = "2005",
language = "Undefined",
isbn = "0169-2690",
series = "Memorandum Afdeling TW",
publisher = "University of Twente",
number = "1760",

}

Post, GF & Woeginger, G 2005, Sports tournaments, home-away assignments, and the break minimization problem. Memorandum Afdeling TW, no. 1760, University of Twente, Enschede.
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

AU - Post, Gerhard F.

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

KW - METIS-225439

KW - IR-65944

KW - EWI-3580

M3 - Report

SN - 0169-2690

T3 - Memorandum Afdeling TW

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

PB - University of Twente

CY - Enschede

ER -

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).