Constrained simultaneous and near-simultaneous embeddings

Fabrizio Frati, Michael Kaufmann, Stephen G. Kobourov

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

5 Scopus citations

Abstract

A geometric simultaneous embedding of two graphs G 1∈= ∈(V 1,E 1) and G 2∈=∈(V 2,E 2) with a bijective mapping of their vertex sets γ: V 1 →V 2 is a pair of planar straight-line drawings Γ 1 of G 1 and Γ 2 of G 2, such that each vertex v 2∈=∈γ(v 1) is mapped in Γ 2 to the same point where v 1 is mapped in Γ 1, where v 1∈ ∈V 1 and v 2∈ ∈V 2. In this paper we examine several constrained versions and a relaxed version of the geometric simultaneous embedding problem. We show that if the input graphs are assumed to share no common edges this does not seem to yield large classes of graphs that can be simultaneously embedded. Further, if a prescribed combinatorial embedding for each input graph must be preserved, then we can answer some of the problems that are still open for geometric simultaneous embedding. Finally, we present some positive and negative results on the near-simultaneous embedding problem, in which vertices are not mapped exactly to the same but to "near" points in the different drawings.

Original languageEnglish (US)
Title of host publicationGraph Drawing - 15th International Symposium, GD 2007, Revised Papers
Pages268-279
Number of pages12
DOIs
StatePublished - Aug 27 2008
Event15th International Symposium on Graph Drawing, GD 2007 - Sydney, Australia
Duration: Sep 24 2007Sep 26 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4875 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Symposium on Graph Drawing, GD 2007
CountryAustralia
CitySydney
Period9/24/079/26/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Frati, F., Kaufmann, M., & Kobourov, S. G. (2008). Constrained simultaneous and near-simultaneous embeddings. In Graph Drawing - 15th International Symposium, GD 2007, Revised Papers (pp. 268-279). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4875 LNCS). https://doi.org/10.1007/978-3-540-77537-9_27