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arXiv · 2201.03813

Asymptotic Optimality of the Greedy Patching Heuristic for Max TSP in Doubling Metrics

Vladimir Shenmaier
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Abstract

The maximum traveling salesman problem (Max~TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. We prove that, in the case when the edge weights are induced by a metric space of bounded doubling dimension, asymptotically optimal solutions of the problem can be found by the simple greedy patching heuristic. Taking as a start point a maximum-weight cycle cover, this heuristic iteratively patches pairs of its cycles into one minimizing the weight loss at each step.

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Vladimir Shenmaier. 2022-01-11. Asymptotic Optimality of the Greedy Patching Heuristic for Max TSP in Doubling Metrics. https://arxiv.org/abs/2201.03813

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