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arXiv · 2309.01902

A $5$-approximation Algorithm for the Traveling Tournament Problem

Jingyang Zhao·Mingyu Xiao
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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 $k\geq 4$ and $n\geq 6$. 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 $k \geq n/2$, the approximation ratio can be improved to $4$.

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Jingyang Zhao, Mingyu Xiao. 2023-09-05. A $5$-approximation Algorithm for the Traveling Tournament Problem. https://arxiv.org/abs/2309.01902

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