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

Authors:
Gerhard Post;Gerhard J. Woeginger
Affiliations:
Department of Applied Mathematics, University Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Discrete Optimization
Year:
2006

Citing 8
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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 14n(n-2) breaks. Secondly, for infinitely many n, we construct opponent schedules for which at least 16n(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=3. This is in strong contrast to the case of r=2 rounds, which can be scheduled (in polynomial time) without any breaks.