Contact representations of graphs in 3D

Jawaherul Alam, William Evans, Stephen Kobourov, Sergey Pupyrev, Jackson Toeniskoetter, Torsten Ueckerdt

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

6 Scopus citations

Abstract

We study contact representations of non-planar graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We present a liner-time algorithm constructing a representation of a 3-connected planar graph, its dual, and the vertex-face incidence graph with 3D boxes. We then investigate contact representations of 1- planar graphs. We first prove that optimal 1-planar graphs without separating 4-cycles admit a contact representation with 3D boxes. However, since not every optimal 1-planar graph can be represented in this way, we also consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graphs with L-shapes.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Ulrike Stege
PublisherSpringer-Verlag
Pages14-27
Number of pages14
ISBN (Print)9783319218397
DOIs
StatePublished - Jan 1 2015
Event14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada
Duration: Aug 5 2015Aug 7 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9214
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Symposium on Algorithms and Data Structures, WADS 2015
CountryCanada
CityVictoria
Period8/5/158/7/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Alam, J., Evans, W., Kobourov, S., Pupyrev, S., Toeniskoetter, J., & Ueckerdt, T. (2015). Contact representations of graphs in 3D. In F. Dehne, J-R. Sack, & U. Stege (Eds.), Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings (pp. 14-27). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214). Springer-Verlag. https://doi.org/10.1007/978-3-319-21840-3_2