The APX-hardness of the Traveling Tournament Problem

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-05-30 DOI:10.1016/j.orl.2025.107311

Jingyang Zhao, Mingyu Xiao

引用次数: 0

Abstract

The Traveling Tournament Problem (TTP-k) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of teams plays each other on two consecutive days, each team plays at most k consecutive home games or away games, and the total traveling distance of all the n teams is minimized. TTP-k allows a polynomial-time approximation scheme when

k = 2

and becomes APX-hard when

k \geq n - 1

. In this paper, we reduce the gap by showing that TTP-k is APX-hard for any fixed

k \geq 3

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旅行比武问题的apx硬度

旅行比赛问题（TTP-k）是体育调度中一个著名的基准问题，它要求我们设计一个双循环赛赛程，使得每对球队在彼此的主场进行一场比赛，没有一对球队连续两天进行比赛，每支球队最多连续进行k场主场比赛或客场比赛，并且所有n支球队的总旅行距离最小。当k=2时，TTP-k允许多项式时间逼近，当k≥n−1时，TTP-k变为APX-hard。在本文中，我们通过证明对于任意固定k≥3，TTP-k是APX-hard来减小这一差距。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

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