On the Complexity of Approximating TSP with Neighborhoods and Related Problems

Shmuel Safra*, Oded Schwartz

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

15 Scopus citations

Abstract

We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the Group-Travelling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the Group-Steiner-Tree in the Euclidean plane and the Minimum Watchman Tour and the Minimum Watchman Path in 3-D. Some inapproximability factors are also shown for special cases of the above problems, where the size of the sets is bounded. Group-TSP and Group-Steiner-Tree where each neighbourhood is connected are also considered. It is shown that approximating these variants to within any constant factor smaller than 2, is NP-hard.

Original languageAmerican English
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsGiuseppe di Battista, Uri Zwick
PublisherSpringer Verlag
Pages446-458
Number of pages13
ISBN (Print)3540200649, 9783540200642
DOIs
StatePublished - 2003
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2832
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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