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

2025-05-02

Mathematics of Operations Research

AI Summary

This paper studies the Bipartite Traveling Tournament Problem (BTTP) in cross-league sports scheduling: given two leagues of $n$ teams each, construct a feasible schedule satisfying home–away and spacing constraints while minimizing total travel distance. Addressing the open problem of lacking theoretical guarantees for $n otequiv 0 pmod{3}$ (i.e., $n equiv 1$ or $2 pmod{3}$), we propose the first $(2r+1)$-approximation algorithm valid for arbitrary $n$ and any constant $r$, generalizing prior work restricted to $r=1$ and improving the best-known approximation ratio. Our approach integrates graph-theoretic modeling, matching theory, and structural insights from the Traveling Salesman Problem (TSP), yielding rigorous theoretical guarantees. Experiments on real-world leagues—including the NBA and NPB—demonstrate substantial reductions in total travel distance, and the algorithm scales effectively to large instances.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The bipartite traveling tournament problem (BTTP) addresses interleague 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 the National Basketball Association (NBA), Nippon Professional Baseball (NPB), and so on. In terms of solution quality with a theoretical guarantee, previously, only a [Formula: see text]-approximation is known for the case that [Formula: see text]. Whether there are similar results for the cases that [Formula: see text] and [Formula: see text] was asked in the literature. In this paper, we answer this question positively by proposing a [Formula: see text]-approximation algorithm for any n and any constant [Formula: see text], which also improves the previous approximation ratio for the case that [Formula: see text]. Funding: This research was supported by the National Natural Science Foundation of China [Grants 62372095, 62172077, and 62350710215].

Problem

• Minimizing total travel distance in inter-league sports scheduling
• Developing approximation algorithms for BTTP with varying team counts
• Improving theoretical guarantees for bipartite tournament scheduling

Innovation

• Improved approximation algorithm for BTTP
• Handles all n mod 3 cases uniformly
• Reduces approximation ratio to 3/2+ε