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
    Volume5664 LNCS
    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)03029743
    ISSN (Electronic)16113349

    Other

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

    Fingerprint

    Electric network analysis
    Dilation
    Computing
    Simple Polygon
    Convex polygon
    Network Analysis
    Euclidean Distance
    Polygon
    Sufficient
    Minimise
    Necessary

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Aronov, B., Buchin, K., Buchin, M., Van Kreveld, M., Löffler, M., Luo, J., ... Speckmann, B. (2009). Connect the dot: Computing feed-links with minimum dilation. In Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings (Vol. 5664 LNCS, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5664 LNCS). https://doi.org/10.1007/978-3-642-03367-4_5

    Connect the dot : Computing feed-links with minimum dilation. / Aronov, Boris; Buchin, Kevin; Buchin, Maike; Van Kreveld, Marc; Löffler, Maarten; Luo, Jun; Silveira, Rodrigo I.; Speckmann, Bettina.

    Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings. Vol. 5664 LNCS 2009. p. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5664 LNCS).

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

    Aronov, B, Buchin, K, Buchin, M, Van Kreveld, M, Löffler, M, Luo, J, Silveira, RI & Speckmann, B 2009, Connect the dot: Computing feed-links with minimum dilation. in Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings. vol. 5664 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5664 LNCS, pp. 49-60, 11th International Symposium on Algorithms and Data Structures, WADS 2009, Banff, AB, Canada, 8/21/09. https://doi.org/10.1007/978-3-642-03367-4_5
    Aronov B, Buchin K, Buchin M, Van Kreveld M, Löffler M, Luo J et al. Connect the dot: Computing feed-links with minimum dilation. In Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings. Vol. 5664 LNCS. 2009. p. 49-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-03367-4_5
    Aronov, Boris ; Buchin, Kevin ; Buchin, Maike ; Van Kreveld, Marc ; Löffler, Maarten ; Luo, Jun ; Silveira, Rodrigo I. ; Speckmann, Bettina. / Connect the dot : Computing feed-links with minimum dilation. Algorithms and Data Structures - 11th International Symposium, WADS 2009, Proceedings. Vol. 5664 LNCS 2009. pp. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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