Approximation algorithms for TSP with neighborhoods in the plane
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.
Cite
@article{arxiv.1703.01640,
title = {Approximation algorithms for TSP with neighborhoods in the plane},
author = {Adrian Dumitrescu and Joseph S. B. Mitchell},
journal= {arXiv preprint arXiv:1703.01640},
year = {2017}
}
Comments
Manuscript that was published in J. Algorithms (2003), with brief clarifying remarks added (2014)