Minimizing breaks by minimizing odd cycle transversals

Koichi Fujii; Tomomi Matsui

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arXiv · 2411.15463

Minimizing breaks by minimizing odd cycle transversals

Koichi Fujii·Tomomi Matsui

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Abstract

Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered undesirable that a team plays consecutive away or home matches; such an occurrence is called a break. Accordingly, it is preferable to reduce the number of breaks in a tournament. A common approach is first to construct a schedule and then determine a home-away assignment based on the given schedule to minimize the number of breaks (first-schedule-then-break). In this study, we concentrate on the problem that arises in the second stage of the first-schedule-then-break approach, namely, the break minimization problem(BMP). We prove that this problem can be reduced to an odd cycle transversal problem, the well-studied graph problem. These results lead to a new approximation algorithm for the BMP.

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Koichi Fujii, Tomomi Matsui. 2024-11-23. Minimizing breaks by minimizing odd cycle transversals. https://arxiv.org/abs/2411.15463

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