Complexity of Traveling Tournament Problem with Trip Length More Than Three

Abstract: The Traveling Tournament Problem is a sports-scheduling problem where the goal is to minimize the total travel distance of teams playing a double round-robin tournament. The constraint 'k' is an imposed upper bound on the number of consecutive home or away matches. It is known that TTP is NP-Hard for k=3 as well as k=infinity. In this work, the general case has been settled by proving that TTP-k is NP-Complete for any fixed k>3.