A 1+O(1/N) approximation algorithm for TTP(2)

TL;DR

This paper introduces the first approximation algorithm with a ratio of 1 + 24/n for the TTP(2), a sports scheduling problem with constraints on consecutive home and away games, improving solution quality.

Contribution

It presents the first 1 + O(1/n) approximation algorithm for TTP(2), addressing a key challenge in sports scheduling with specific constraints.

Findings

Approximation ratio of 1 + 24/n for TTP(2)

First algorithm achieving 1 + O(1/n) ratio for this problem

Provides a scalable solution for large number of teams

Abstract

The traveling tournament problem is a well-known benchmark problem of the sports scheduling. We propose an approximation algorithm for the traveling tournament problem with the constraints such that both the number of consecutive home games and that of consecutive away games are at most two (called TTP(2)). The approximation ratio of the proposed algorithm is 1 + 24/n for n teams, which is the first 1 + O(1/n) approximation algorithm for TTP(2).