On approximating the TSP with intersecting neighborhoods

K.M. Elbassioni, A.V. Fishkin, R.A. Sitters

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

    16 Citations (Scopus)


    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 languageEnglish
    Title of host publicationAlgorithms and Computation
    Subtitle of host publication17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006. Proceedings
    EditorsT. Asano
    Place of PublicationBerlin
    Number of pages10
    ISBN (Electronic)978-3-540-49696-0
    ISBN (Print)3-540-49694-7, 978-3-540-49694-6
    Publication statusPublished - 2006

    Publication series

    NameLecture Notes in Computer Science
    ISSN (Print)0302-9743


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