A Further Improvement on Approximating TTP-2

TL;DR

This paper presents an improved approximation algorithm for the TTP-2 sports scheduling problem, reducing the approximation ratio for even team counts and demonstrating better results on benchmark instances.

Contribution

It introduces a new algorithm that improves the approximation ratio from (1+4/n) to (1+3/n) for even n/2 in TTP-2, with enhanced experimental performance.

Findings

Improved approximation ratio from (1+4/n) to (1+3/n) for even n/2.

Algorithm outperforms previous methods on all benchmark instances with even n/2.

Achieves 1% to 4% improvement over previous results.

Abstract

The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, minimizing the total distance traveled by all $n$ teams ($n$ is even). In this paper, we consider TTP-2, i.e., TTP with one more constraint that each team can have at most two consecutive home games or away games. Due to the different structural properties, known algorithms for TTP-2 are different for $n/2$ being odd and even. For odd $n/2$, the best known approximation ratio is about $(1+12/n)$, and for even $n/2$, the best known approximation ratio is about $(1+4/n)$. In this paper, we further improve the approximation ratio from $(1+4/n)$ to $(1+3/n)$ for $n/2$ being even. Experimental results on benchmark sets show that our algorithm can improve previous results on all instances with even $n/2$ by $1\%$ to $4\%$.