Star unfolding of a polytope with applications

Pankaj K. Agarwal, Boris Aronov, Joseph O’Rourke, Catherine A. Schevon

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We define the notion of a “star unfolding” of the surface P of a convex polytope with n vertices and use it to construct an algorithm for computing a small superset of the set of all sequences of edges traversed by shortest paths on P. It requires O(n6) time and produces O(n8) sequences, thereby improving an earlier algorithm of Sharir that in O(n8 log n) time produces O(n7) sequences, A variant of our algorithm runs in O(n5 log n) time and produces a more compact representation of size O(n5) for the same set of O(n6) sequences. In addition, we describe an O(n10) time procedure for computing the geodesic diameter of P, which is the maximum possible separation of two points on P, with the distance measured along P, improving an earlier O(n14 log n) algorithm of O’Rourke and Schevon.

    Original languageEnglish (US)
    Title of host publicationSWAT 1990 - 2nd Scandinavian Workshop on Algorithm Theory, Proceedings
    EditorsRolf Karlsson, John R. Gilbert
    PublisherSpringer Verlag
    Pages251-263
    Number of pages13
    ISBN (Print)9783540528463
    DOIs
    StatePublished - 1990
    Event2nd Scandinavian Workshop on Algorithm Theory, SWAT 1990 - Bergen, Norway
    Duration: Jul 11 1990Jul 14 1990

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume447 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other2nd Scandinavian Workshop on Algorithm Theory, SWAT 1990
    CountryNorway
    CityBergen
    Period7/11/907/14/90

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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