Simultaneous embedding of a planar graph and its dual on the grid

Cesim Erten, Stephen G Kobourov

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

7 Citations (Scopus)

Abstract

Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the dual graph should cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual on a small integer grid such that the edges are drawn as straight-line segments and the only crossings are between primal-dual pairs of edges. We provide an O(n) time algorithm that simultaneously embeds a 3-connected planar graph and its dual on a (2n - 2) × (2n - 2) integer grid, where n is the total number of vertices in the graph and its dual.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages575-587
Number of pages13
Volume2518 LNCS
DOIs
StatePublished - 2002
Event13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 - Vancouver, BC, Canada
Duration: Nov 21 2002Nov 23 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2518 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th Annual International Symposium on Algorithms and Computation, ISAAC 2002
CountryCanada
CityVancouver, BC
Period11/21/0211/23/02

Fingerprint

Planar graph
Grid
Dual Graph
Integer
Primal-dual
Graph in graph theory
Line segment
Straight Line
Connected graph
Face
Requirements

Keywords

  • Convex planar drawing
  • Graph drawing
  • Planar embedding
  • Simultaneous embedding

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Erten, C., & Kobourov, S. G. (2002). Simultaneous embedding of a planar graph and its dual on the grid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 575-587). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS). https://doi.org/10.1007/3-540-36136-7_50

Simultaneous embedding of a planar graph and its dual on the grid. / Erten, Cesim; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2518 LNCS 2002. p. 575-587 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2518 LNCS).

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

Erten, C & Kobourov, SG 2002, Simultaneous embedding of a planar graph and its dual on the grid. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2518 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2518 LNCS, pp. 575-587, 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, Vancouver, BC, Canada, 11/21/02. https://doi.org/10.1007/3-540-36136-7_50
Erten C, Kobourov SG. Simultaneous embedding of a planar graph and its dual on the grid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2518 LNCS. 2002. p. 575-587. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-36136-7_50
Erten, Cesim ; Kobourov, Stephen G. / Simultaneous embedding of a planar graph and its dual on the grid. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2518 LNCS 2002. pp. 575-587 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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