Complexity of Traveling Tournament Problem with Trip Length More Than Three

TL;DR

This paper proves that the Traveling Tournament Problem with a maximum of more than three consecutive home or away matches is NP-Complete, extending the known computational complexity results for this sports scheduling problem.

Contribution

It establishes that TTP-k is NP-Complete for all fixed k > 3, resolving the complexity status for the general case.

Findings

TTP-k is NP-Complete for any fixed k > 3.

The problem is NP-Hard for k=3 and k=infinity.

The complexity classification is extended to all k > 3.

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.