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

Gerhard F. Post, Gerhard Woeginger

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)
33 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)165-173
Number of pages9
JournalDiscrete optimization
Volume3
Issue numberWP06-03/2
DOIs
Publication statusPublished - 1 Jun 2006

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