Probabilistic Analysis of Edge Elimination for Euclidean TSP

09/27/2018

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by   Xianghui Zhong, et al.

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One way to speed up the calculation of optimal TSP tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so several edge elimination approaches have been proposed in the past. In this paper we investigate two of them in the scenario where the input consists of n uniformly random points. We show that after the edge elimination procedure of Hougardy and Schroeder the expected number of remaining edges is Θ(n), while after that of Jonker and Volgenant the expected number of remaining edges is Θ(n^2).