On approximating the TSP with intersecting neighborhoods

Khaled Elbassioni, Aleksei V. Fishkin, René Sitters

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations


In the TSP with neighborhoods problem we are given a set of n regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give two approximation algorithms for the case when the regions are allowed to intersect: We give the first O(1)-factor approximation algorithm for intersecting convex fat objects of comparable diameters where we are allowed to hit each object only at a finite set of specified points. The proof follows from two packing lemmas that are of independent interest. For the problem in its most general form (but without the specified points restriction) we give a simple O(logn)-approximation algorithm.

Original languageBritish English
Title of host publicationAlgorithms and Computation - 17th International Symposium, ISAAC 2006, Proceedings
Number of pages10
StatePublished - 2006
Event17th International Symposium on Algorithms and Computation, ISAAC 2006 - Kolkata, India
Duration: 18 Dec 200620 Dec 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4288 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Symposium on Algorithms and Computation, ISAAC 2006


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