Asymptotic Optimality of the Greedy Patching Heuristic for Max TSP in Doubling Metrics
Data Structures and Algorithms
2022-01-12 v1 Computational Geometry
Discrete Mathematics
Combinatorics
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2201.03813,
title = {Asymptotic Optimality of the Greedy Patching Heuristic for Max TSP in Doubling Metrics},
author = {Vladimir Shenmaier},
journal= {arXiv preprint arXiv:2201.03813},
year = {2022}
}