A 5-approximation Algorithm for the Traveling Tournament Problem
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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≥ 4 and 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 ≥ n/2, the approximation ratio can be improved to 4.
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