Practical Algorithms with Guaranteed Approximation Ratio for TTP with Maximum Tour Length Two

TL;DR

This paper introduces practical algorithms for the Traveling Tournament Problem with maximum two consecutive home or away games, achieving improved approximation ratios and better solutions in experiments.

Contribution

The authors develop new algorithms for TTP-2 with improved approximation ratios for both odd and even cases, and demonstrate their effectiveness through experiments.

Findings

Approximation ratio for even n/2 improved to 1+3/n

Approximation ratio for odd n/2 improved to 1+5/n

Algorithms outperform previous solutions with an average 5.66% improvement

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 under the constraint that at most two consecutive home games or away games are allowed for each team. We propose practical algorithms for TTP-2 with improved approximation ratios. Due to the different structural properties of the problem, all known algorithms for TTP-2 are different for $n/2$ being odd and even, and our algorithms are also different for these two cases. For even $n/2$, our approximation ratio is $1+3/n$, improving the previous result of $1+4/n$. For odd $n/2$, our approximation ratio is $1+5/n$, improving the previous result of $3/2+6/n$. In practice, our algorithms are easy to implement. Experiments on well-known benchmark sets show that our algorithms beat previously known solutions for all instances with an average improvement of $5.66\%$.