Minimizing breaks by minimizing odd cycle transversals

TL;DR

This paper addresses the problem of minimizing breaks in sports tournament schedules by reducing it to an odd cycle transversal problem, providing a new approximation algorithm for this challenge.

Contribution

It introduces a novel reduction of the break minimization problem to the odd cycle transversal problem and develops a new approximation algorithm.

Findings

The break minimization problem can be reduced to an odd cycle transversal problem.

A new approximation algorithm for the break minimization problem is proposed.

The approach improves scheduling efficiency by reducing breaks in tournaments.

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.