### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente |

Number of pages | 14 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 2005 |

### Publication series

Name | Memorandum Afdeling TW |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1760 |

ISSN (Print) | 0169-2690 |

### Keywords

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

### Cite this

*Sports tournaments, home-away assignments, and the break minimization problem*. (Memorandum Afdeling TW; No. 1760). Enschede: University of Twente.

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*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.

Research output: Book/Report › Report › Professional

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 -