The Traveling Tournament Problem
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In this thesis we study the Traveling Tournament problem (TTP) which asks to generate a feasible schedule for a sports league such that the total travel distance incurred by all teams throughout the season is minimized. Throughout our three technical chapters a wide range of topics connected to the TTP are explored. We begin by considering the computational complexity of the problem. Despite existing results on the NP-hardness of TTP, the question of whether or not TTP is also APX-hard was an unexplored area in the literature. We prove the affirmative by constructing an L-reduction from (1,2)-TSP to TTP. To reach the desired result, we show that given an instance of TSP with a solution of cost K, we can construct an instance of TTP with a solution of cost at most 20m(m+1)cK where m = c(n-1)+1, n is the number of teams, and c > 5, c ∈ ℤ is fixed. On the other hand, we show that given a feasible schedule to the constructed TTP instance, we can recover a tour on the original TSP instance. The next chapter delves into a popular variation of the problem, the mirrored TTP, which has the added stipulation that the first and second half of the schedule have the same order of match-ups. Building upon previous techniques, we present an approximation algorithm for constructing a mirrored double round-robin schedule under the constraint that the number of consecutive home or away games is at most two. We achieve an approximation ratio on the order of 3/2 + O(1)/n. Lastly, we present a survey of local search methods for solving TTP and discuss the performance of these techniques on benchmark instances.
Cite this version of the work
Salomon Bendayan (2022). The Traveling Tournament Problem. UWSpace. http://hdl.handle.net/10012/18553