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8140 Sports tournaments, home-away assignments, and the break minimization problem
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Post, G.F. and Woeginger, G.J. (2006) Sports tournaments, home-away assignments, and the break minimization problem. Discrete Optimization, 3 (2). pp. 165-173. ISSN 1572-5286 *** ISI Impact 0,500 ***

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Official URL: http://dx.doi.org/10.1016/j.disopt.2005.08.009

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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 ${1\over 4}n(n-2)$ breaks. Secondly, for infinitely many $n$, we construct opponent schedules for which at least ${1\over 6}n(n-1)$ 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 $r\ge 3$. This is in strong contrast to the case of $r=2$ rounds, which can be scheduled (in polynomial time) without any breaks.

Item Type:Article
Research Group:EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:CTIT-eProductivity
Research Project:BRICKS/IS3: Decision Support Systems for Logistic Networks and Supply Chain Optimization
ID Code:8140
Status:Published
Deposited On:21 December 2006
Refereed:Yes
International:Yes
ISI Impact Factor:0,500
More Information:statisticsmetis

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