A fast approximation algorithm for TSP with neighborhoods and red-blue separation

Christos Levcopoulos, Joachim Gudmundsson

    Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceedingPeer review

    Sammanfattning

    In TSP with neighborhoods (TSPN) we are given a collec-tion X of k polygonal regions, called neighborhoods, with totally n ver-tices, and we seek the shortest tour that visits each neighborhood. TheEuclidean TSP is a special case of the TSPN problem, so TSPN is alsoNP-hard. In this paper we present a simple and fast algorithm that, givena start point, computes a TSPN tour of length O(log k) times the opti-mum in time O(n+k log k). When no start point is given we show howto compute a good start point in time O(n2 log n), hence we obtain alogarithmic approximation algorithm that runs in time O(n2 log n). Wealso present an algorithm which performs at least one of the followingtwo tasks (which of these tasks is performed depends on the given input):(1) It outputs in time O(n log n) a TSPN tour of length O(log k) timesthe optimum. (2) It outputs a TSPN tour of length less than (1+) timesthe optimum in cubic time, where is an arbitrary real constant givenas an optional parameter.The results above are signicant improvements, since the best previouslyknown logarithmic approximation algorithm runs in (n5) time in theworst case.
    Originalspråkengelska
    Titel på värdpublikationComputing and combinatorics / Lecture notes in computer science
    RedaktörerTakano Asano
    FörlagSpringer
    Sidor473-482
    Volym1627
    DOI
    StatusPublished - 1999
    Evenemang5th annual international conference, COCOON '99 - Tokyo, Japan
    Varaktighet: 1999 juli 261999 juli 28

    Publikationsserier

    Namn
    Volym1627

    Konferens

    Konferens5th annual international conference, COCOON '99
    Land/TerritoriumJapan
    OrtTokyo
    Period1999/07/261999/07/28

    Ämnesklassifikation (UKÄ)

    • Datavetenskap (datalogi)

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