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arXiv · 1909.12025

The Approximation Ratio of the 2-Opt Heuristic for the Metric Traveling Salesman Problem

Stefan Hougardy·Fabian Zaiser·Xianghui Zhong
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Abstract

The 2-Opt heuristic is one of the simplest algorithms for finding good solutions to the metric Traveling Salesman Problem. It is the key ingredient to the well-known Lin-Kernighan algorithm and often used in practice. So far, only upper and lower bounds on the approximation ratio of the 2-Opt heuristic for the metric TSP were known. We prove that for the metric TSP with $n$ cities, the approximation ratio of the 2-Opt heuristic is $\sqrt{n/2}$ and that this bound is tight.

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Stefan Hougardy, Fabian Zaiser, Xianghui Zhong. 2019-09-26. The Approximation Ratio of the 2-Opt Heuristic for the Metric Traveling Salesman Problem. https://arxiv.org/abs/1909.12025

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