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

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 languageEnglish
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

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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