An Improved Algorithm for a Bipartite Traveling Tournament in Interleague Sports Scheduling

TL;DR

This paper introduces a new approximation algorithm for the bipartite traveling tournament problem, improving solution quality and providing guarantees for all cases of team league sizes, thus advancing inter-league sports scheduling methods.

Contribution

The paper presents a $(3/2+ ext{ε})$-approximation algorithm applicable to all team sizes, extending previous results limited to specific cases and improving approximation ratios.

Findings

Provides a $(3/2+ ext{ε})$-approximation algorithm for BTTP.

Achieves solution quality guarantees for all team sizes.

Improves previous approximation ratios for specific cases.

Abstract

The bipartite traveling tournament problem (BTTP) addresses inter-league sports scheduling, which aims to design a feasible bipartite tournament between two $n$-team leagues under some constraints such that the total traveling distance of all participating teams is minimized. Since its introduction, several methods have been developed to design feasible schedules for NBA, NPB and so on. In terms of solution quality with a theoretical guarantee, previously only a $(2+\varepsilon)$-approximation is known for the case that $n\equiv 0 \pmod 3$. Whether there are similar results for the cases that $n\equiv 1 \pmod 3$ and $n\equiv 2 \pmod 3$ was asked in the literature. In this paper, we answer this question positively by proposing a $(3/2+\varepsilon)$-approximation algorithm for any $n$ and any constant $\varepsilon>0$, which also improves the previous approximation ratio for the case that $n\equiv 0 \pmod 3$.