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

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

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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
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Discrete Mathematics and Mathematical Programming (DMMP)
Link to this item:	http://purl.utwente.nl/publications/63682
Official URL:	http://dx.doi.org/10.1016/j.disopt.2005.08.009
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