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