Simultaneous graph embedding with bends and circular arcs

Justin Cappos, Alejandro Estrella-Balderrama, J. Joseph Fowler, Stephen G. Kobourov

    Research output: Contribution to journalArticle

    Abstract

    A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.

    Original languageEnglish (US)
    Pages (from-to)173-182
    Number of pages10
    JournalComputational Geometry: Theory and Applications
    Volume42
    Issue number2
    DOIs
    StatePublished - Feb 2009

    Fingerprint

    Graph Embedding
    Stars
    Arc of a curve
    Outerplanar Graph
    Path
    Planar graph
    Point Sets
    Set of points
    Star
    Graph in graph theory
    Vertex of a graph
    Demonstrate

    Keywords

    • Simultaneous embedding

    ASJC Scopus subject areas

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

    Cite this

    Simultaneous graph embedding with bends and circular arcs. / Cappos, Justin; Estrella-Balderrama, Alejandro; Fowler, J. Joseph; Kobourov, Stephen G.

    In: Computational Geometry: Theory and Applications, Vol. 42, No. 2, 02.2009, p. 173-182.

    Research output: Contribution to journalArticle

    Cappos, J, Estrella-Balderrama, A, Fowler, JJ & Kobourov, SG 2009, 'Simultaneous graph embedding with bends and circular arcs', Computational Geometry: Theory and Applications, vol. 42, no. 2, pp. 173-182. https://doi.org/10.1016/j.comgeo.2008.05.003
    Cappos, Justin ; Estrella-Balderrama, Alejandro ; Fowler, J. Joseph ; Kobourov, Stephen G. / Simultaneous graph embedding with bends and circular arcs. In: Computational Geometry: Theory and Applications. 2009 ; Vol. 42, No. 2. pp. 173-182.
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