{"title":"A 5-approximation algorithm for the traveling tournament problem","authors":"Jingyang Zhao, Mingyu Xiao","doi":"10.1007/s10479-025-06483-1","DOIUrl":null,"url":null,"abstract":"<div><p>The Traveling Tournament Problem (TTP-<i>k</i>) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all <i>n</i> teams is minimized under the constraints that each pair of teams plays one game in each other’s home venue, and each team plays at most <i>k</i>-consecutive home games or away games. Westphal and Noparlik (Ann. Oper. Res. 218(1):347-360, 2014) claimed a 5.875-approximation algorithm for all <span>\\(k\\ge 4\\)</span> and <span>\\(n\\ge 6\\)</span>. However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a 5-approximation algorithm for all <i>k</i> and <i>n</i>. Furthermore, if <span>\\(k \\ge n/2\\)</span>, the approximation ratio can be improved to 4.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"346 3","pages":"2287 - 2305"},"PeriodicalIF":4.4000,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06483-1","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
The Traveling Tournament Problem (TTP-k) is a well-known benchmark problem in tournament timetabling, which asks us to design a double round-robin schedule such that the total traveling distance of all n teams is minimized under the constraints that each pair of teams plays one game in each other’s home venue, and each team plays at most k-consecutive home games or away games. Westphal and Noparlik (Ann. Oper. Res. 218(1):347-360, 2014) claimed a 5.875-approximation algorithm for all \(k\ge 4\) and \(n\ge 6\). However, there were both flaws in the construction of the schedule and in the analysis. In this paper, we show that there is a 5-approximation algorithm for all k and n. Furthermore, if \(k \ge n/2\), the approximation ratio can be improved to 4.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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