Witness (Delaunay) graphs

Boris Aronov, Muriel Dulieu, Ferran Hurtado

    Research output: Contribution to journalArticle

    Abstract

    Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.

    Original languageEnglish (US)
    Pages (from-to)329-344
    Number of pages16
    JournalComputational Geometry: Theory and Applications
    Volume44
    Issue number6-7
    DOIs
    StatePublished - Aug 2011

    Fingerprint

    Delaunay
    Proximity Graphs
    Graph Drawing
    Graph in graph theory
    Geometric object
    Graph Representation
    Point Sets
    Discrimination
    Flexibility
    Generalization

    Keywords

    • Delaunay graph
    • Graph drawing
    • Proximity graphs
    • Witness graphs

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Science Applications
    • Computational Mathematics
    • Control and Optimization
    • Geometry and Topology

    Cite this

    Witness (Delaunay) graphs. / Aronov, Boris; Dulieu, Muriel; Hurtado, Ferran.

    In: Computational Geometry: Theory and Applications, Vol. 44, No. 6-7, 08.2011, p. 329-344.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Dulieu, Muriel ; Hurtado, Ferran. / Witness (Delaunay) graphs. In: Computational Geometry: Theory and Applications. 2011 ; Vol. 44, No. 6-7. pp. 329-344.
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