Connect the dot: Computing feed-links with minimum dilation

Boris Aronov, Kevin Buchin, Maike Buchin, Marc Van Kreveld, Maarten Löffler, Jun Luo, Rodrigo I. Silveira, Bettina Speckmann

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

    Abstract

    A feed-link is an artificial connection from a given location p to a real-world network. It is most commonly added to an incomplete network to improve the results of network analysis, by making p part of the network. The feed-link has to be "reasonable", hence we use the concept of dilation to determine the quality of a connection. We consider the following abstract problem: Given a simple polygon P with n vertices and a point p inside, determine a point q on P such that adding a feedlink minimizes the maximum dilation of any point on P. Here the dilation of a point r on P is the ratio of the shortest route from r over P and to p, to the Euclidean distance from r to p. We solve this problem in O(λ 7(n)logn) time, where λ 7(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7. We also show that for convex polygons, two feed-links are always sufficient and sometimes necessary to realize constant dilation, and that k feed-links lead to a dilation of 1 + O(1/k). For (α,β)-covered polygons, a constant number of feed-links suffices to realize constant dilation.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings
    Pages49-60
    Number of pages12
    DOIs
    StatePublished - 2009
    Event11th International Symposium on Algorithms and Data Structures, WADS 2009 - Banff, AB, Canada
    Duration: Aug 21 2009Aug 23 2009

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5664 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other11th International Symposium on Algorithms and Data Structures, WADS 2009
    CountryCanada
    CityBanff, AB
    Period8/21/098/23/09

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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