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arXiv · 1412.7366

The Approximation Ratio of the Greedy Algorithm for the Metric Traveling Salesman Problem

Judith Brecklinghaus·Stefan Hougardy
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Abstract

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is $\Theta(\log n)$. Moreover, we prove that the same result also holds for graphic, Euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the Clarke-Wright savings heuristic for the metric Traveling Salesman Problem is $\Theta(\log n)$.

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Judith Brecklinghaus, Stefan Hougardy. 2014-12-23. The Approximation Ratio of the Greedy Algorithm for the Metric Traveling Salesman Problem. https://arxiv.org/abs/1412.7366

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