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arXiv · 1703.01640

Approximation algorithms for TSP with neighborhoods in the plane

Adrian Dumitrescu·Joseph S. B. Mitchell
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Abstract

In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this paper, we present new approximation results for the TSPN, including (1) a constant-factor approximation algorithm for the case of arbitrary connected neighborhoods having comparable diameters; and (2) a PTAS for the important special case of disjoint unit disk neighborhoods (or nearly disjoint, nearly-unit disks). Our methods also yield improved approximation ratios for various special classes of neighborhoods, which have previously been studied. Further, we give a linear-time O(1)-approximation algorithm for the case of neighborhoods that are (infinite) straight lines.

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Adrian Dumitrescu, Joseph S. B. Mitchell. 2017-03-05. Approximation algorithms for TSP with neighborhoods in the plane. https://doi.org/10.1016/s0196-6774(03)00047-6

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