Sparse geometric graphs with small dilation

Boris Aronov, Mark De Berg, Otfried Cheong, Joachim Gudmundsson, Herman Haverkort, Antoine Vigneron

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

    Abstract

    Given a set S of n points in the plane, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, and dilation O(n/(k + 1)) can be computed in time O(n log n). We also construct n-point sets for which any geometric graph with n - 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings
    Pages50-59
    Number of pages10
    Volume3827 LNCS
    DOIs
    StatePublished - 2005
    Event16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China
    Duration: Dec 19 2005Dec 21 2005

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume3827 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other16th International Symposium on Algorithms and Computation, ISAAC 2005
    CountryChina
    CityHainan
    Period12/19/0512/21/05

    Fingerprint

    Geometric Graphs
    Sparse Graphs
    Dilation
    Dilatation
    Point Sets
    Integer
    Vertex of a graph

    ASJC Scopus subject areas

    • Computer Science(all)
    • Biochemistry, Genetics and Molecular Biology(all)
    • Theoretical Computer Science

    Cite this

    Aronov, B., De Berg, M., Cheong, O., Gudmundsson, J., Haverkort, H., & Vigneron, A. (2005). Sparse geometric graphs with small dilation. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings (Vol. 3827 LNCS, pp. 50-59). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). https://doi.org/10.1007/11602613_7

    Sparse geometric graphs with small dilation. / Aronov, Boris; De Berg, Mark; Cheong, Otfried; Gudmundsson, Joachim; Haverkort, Herman; Vigneron, Antoine.

    Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. Vol. 3827 LNCS 2005. p. 50-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS).

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

    Aronov, B, De Berg, M, Cheong, O, Gudmundsson, J, Haverkort, H & Vigneron, A 2005, Sparse geometric graphs with small dilation. in Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. vol. 3827 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, pp. 50-59, 16th International Symposium on Algorithms and Computation, ISAAC 2005, Hainan, China, 12/19/05. https://doi.org/10.1007/11602613_7
    Aronov B, De Berg M, Cheong O, Gudmundsson J, Haverkort H, Vigneron A. Sparse geometric graphs with small dilation. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. Vol. 3827 LNCS. 2005. p. 50-59. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11602613_7
    Aronov, Boris ; De Berg, Mark ; Cheong, Otfried ; Gudmundsson, Joachim ; Haverkort, Herman ; Vigneron, Antoine. / Sparse geometric graphs with small dilation. Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. Vol. 3827 LNCS 2005. pp. 50-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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