Contact representations of graphs in 3D

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

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

6 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages14-27
Number of pages14
Volume9214
ISBN (Print)9783319218397
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Planar graph
Contact
Polyhedron
Graph in graph theory
Connected graph
Incidence
Face
Cycle
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, J., Evans, W., Kobourov, S. G., Pupyrev, S., Toeniskoetter, J., & Ueckerdt, T. (2015). Contact representations of graphs in 3D. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9214, 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

Contact representations of graphs in 3D. / Alam, Jawaherul; Evans, William; Kobourov, Stephen G; Pupyrev, Sergey; Toeniskoetter, Jackson; Ueckerdt, Torsten.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9214 Springer Verlag, 2015. p. 14-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214).

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

Alam, J, Evans, W, Kobourov, SG, Pupyrev, S, Toeniskoetter, J & Ueckerdt, T 2015, Contact representations of graphs in 3D. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9214, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9214, Springer Verlag, pp. 14-27, 14th International Symposium on Algorithms and Data Structures, WADS 2015, Victoria, Canada, 8/5/15. https://doi.org/10.1007/978-3-319-21840-3_2
Alam J, Evans W, Kobourov SG, Pupyrev S, Toeniskoetter J, Ueckerdt T. Contact representations of graphs in 3D. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9214. Springer Verlag. 2015. p. 14-27. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-21840-3_2
Alam, Jawaherul ; Evans, William ; Kobourov, Stephen G ; Pupyrev, Sergey ; Toeniskoetter, Jackson ; Ueckerdt, Torsten. / Contact representations of graphs in 3D. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9214 Springer Verlag, 2015. pp. 14-27 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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