Planarity-preserving clustering and embedding for large planar graphs?

Christian A. Duncan, Michael T. Goodrich, Stephen G Kobourov

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

15 Citations (Scopus)

Abstract

In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer's mental map. The overall running time of the algorithm is O(n log n), where n is the number of vertices of graph G.

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
Pages186-196
Number of pages11
Volume1731
ISBN (Print)3540669043, 9783540669043
DOIs
StatePublished - 1999
Externally publishedYes
Event7th International Symposium on Graph Drawing, GD 1999 - Prague, Czech Republic
Duration: Sep 15 1999Sep 19 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1731
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Symposium on Graph Drawing, GD 1999
CountryCzech Republic
CityPrague
Period9/15/999/19/99

Fingerprint

Drawing (graphics)
Planarity
Planar graph
Clustering
Graph in graph theory
Arbitrary

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (1999). Planarity-preserving clustering and embedding for large planar graphs? In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1731, pp. 186-196). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1731). Springer Verlag. https://doi.org/10.1007/3-540-46648-7_19

Planarity-preserving clustering and embedding for large planar graphs? / Duncan, Christian A.; Goodrich, Michael T.; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731 Springer Verlag, 1999. p. 186-196 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1731).

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

Duncan, CA, Goodrich, MT & Kobourov, SG 1999, Planarity-preserving clustering and embedding for large planar graphs? in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1731, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1731, Springer Verlag, pp. 186-196, 7th International Symposium on Graph Drawing, GD 1999, Prague, Czech Republic, 9/15/99. https://doi.org/10.1007/3-540-46648-7_19
Duncan CA, Goodrich MT, Kobourov SG. Planarity-preserving clustering and embedding for large planar graphs? In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731. Springer Verlag. 1999. p. 186-196. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-46648-7_19
Duncan, Christian A. ; Goodrich, Michael T. ; Kobourov, Stephen G. / Planarity-preserving clustering and embedding for large planar graphs?. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731 Springer Verlag, 1999. pp. 186-196 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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