A Further Improvement on Approximating TTP-2

Jingyang Zhao, Mingyu Xiao

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 $$4\%$$ .