On the Approximation Ratio of the 3-Opt Algorithm for the (1,2)-TSP

02/28/2021

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by   Xianghui Zhong, et al.

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The (1,2)-TSP is a special case of the TSP where each edge has cost either 1 or 2. In this paper we give a lower bound of 3/2 for the approximation ratio of the 2-Opt algorithm for the (1,2)-TSP. Moreover, we show that the 3-Opt algorithm has an exact approximation ratio of 11/8 for the (1,2)-TSP. Furthermore, we introduce the 3-Opt++-algorithm, an improved version of the 3-Opt algorithm for the (1-2)-TSP with an exact approximation ratio of 4/3.