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 Scopus citations

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 publicationAlgorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings
Pages575-587
Number of pages13
DOIs
StatePublished - Dec 1 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Erten, C., & Kobourov, S. G. (2002). Simultaneous embedding of a planar graph and its dual on the grid. In Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings (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