## Approximation algorithms for TSP with neighborhoods in the plane (2001)

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Venue: | J. ALGORITHMS |

Citations: | 67 - 9 self |

### BibTeX

@INPROCEEDINGS{Dumitrescu01approximationalgorithms,

author = {Adrian Dumitrescu and Joseph S. B. Mitchell},

title = {Approximation algorithms for TSP with neighborhoods in the plane},

booktitle = {J. ALGORITHMS},

year = {2001},

pages = {38--46},

publisher = {}

}

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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 (innite) straight lines.