An Improved Approximation Algorithm for the Traveling Tournament Problem

This paper describes the traveling tournament problem, a well‐known benchmark problem in the field of tournament timetabling. We propose an approximation algorithm for the traveling tournament problem with the constraints such that both the number of consecutive away games and that of consecutive home games are at most k. When k≤5, the approximation ratio of the proposed algorithm is bounded by (2k−1)/k+O(k/n) where n denotes the number of teams; when k>5, the ratio is bounded by (5k−7)/(2k)+O(k/n). For k=3, the most investigated case of the traveling tournament problem to date, the approximation ratio of the proposed algorithm is 5/3+O(1/n); this is better than the previous approximation algorithm proposed for k=3, whose approximation ratio is 2+O(1/n).