A 5-approximation algorithm for the traveling tournament problem

Jingyang Zhao () and Mingyu Xiao ()
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Jingyang Zhao: University of Electronic Science and Technology of China
Mingyu Xiao: University of Electronic Science and Technology of China

Annals of Operations Research, 2025, vol. 346, issue 3, No 12, 2287-2305

Abstract: 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 $$k\ge 4$$ k ≥ 4 and $$n\ge 6$$ n ≥ 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 $$k \ge n/2$$ k ≥ n / 2 , the approximation ratio can be improved to 4.

Keywords: Approximation algorithms; Sports scheduling; Traveling tournament problem; Timetabling; Combinatorial optimization (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06483-1

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