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

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Post, G.F. and Woeginger, G.J. (2005) Sports tournaments, home-away assignments, and the break minimization problem. [Report]

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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.
Item Type:Report
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65944
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