The maximum traveling salesman problem under polyhedral norms

A.I. Barvinok, D.S. Johnson, G.J. Woeginger, R. Woodroofe

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

    32 Citations (Scopus)

    Abstract

    We consider the traveling salesman problem when the cities are points in Rd for some fixed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n f-2 log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n 2 log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NP-hard.
    Original languageEnglish
    Title of host publicationInteger Programming and Combinatorial Optimization (Proceedings 6th International IPCO Conference, Houston TX, USA, June 22-24, 1998)
    EditorsR.E. Bixby, E.A. Boyd, R.Z. Rios-Mercado
    Place of PublicationBerlin
    PublisherSpringer
    Pages195-201
    DOIs
    Publication statusPublished - 1998

    Publication series

    NameLecture Notes in Computer Science
    Volume1412
    ISSN (Print)0302-9743

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