The APX-hardness of the Traveling Tournament Problem

08/27/2023

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by   Jingyang Zhao, et al.

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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, 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 PTAS when k=2 and becomes APX-hard when k≥ n-1. In this paper, we reduce the gap by showing that TTP-k is APX-hard for any fixed k≥3.