Drawing with fat edges

Christian A. Duncan, Alon Efrat, Stephen G. Kobourov, Carola Wenk

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

14 Scopus citations

Abstract

In this paper, we introduce the problem of drawing with "fat" edges. Traditionally, graph drawing algorithms represent vertices as circles and edges as closed curves connecting the vertices. In this paper we consider the problem of drawing graphs with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information. We present a model for drawing with fat edges and a corresponding polynomial time algorithm that uses the model. We focus on a restricted class of graphs that occur in VLSI wire routing and show how to extend the algorithm to general planar graphs. We show how to take an arbitrary wire routing and convert it into a homotopic equivalent routing such that the distance between any two wires is maximized. Moreover, the routing uses the minimum length wires. Maximizing the distance between wires is equivalent to finding the drawing in which the edges are drawn as thick as possible. To the best of our knowledge this is the first algorithm that finds the maximal distance between any two wires and allows for wires of variable thickness. The previous best known result for the corresponding decision problem with unit wire thickness is the algorithm of Gao et al, which runs in O(kn2 log(kn)) time and uses O(kn2) space, where n is the number of wires and k is the maximum of the input and output complexities. The running time of our algorithm is O(kn + n3) and the space required is O(k+n). The algorithm generalizes naturally to general planar graphs as well.

Original languageEnglish (US)
Title of host publicationGraph Drawing - 9th International Symposium, GD 2001, Revised Papers
EditorsPetra Mutzel, Michael Junger, Sebastian Leipert
PublisherSpringer-Verlag
Pages162-177
Number of pages16
ISBN (Print)3540433090, 9783540433095
DOIs
StatePublished - Jan 1 2002
Event9th International Symposium on Graph Drawing, GD 2001 - Vienna, Austria
Duration: Sep 23 2001Sep 26 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2265 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th International Symposium on Graph Drawing, GD 2001
CountryAustria
CityVienna
Period9/23/019/26/01

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Duncan, C. A., Efrat, A., Kobourov, S. G., & Wenk, C. (2002). Drawing with fat edges. In P. Mutzel, M. Junger, & S. Leipert (Eds.), Graph Drawing - 9th International Symposium, GD 2001, Revised Papers (pp. 162-177). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2265 LNCS). Springer-Verlag. https://doi.org/10.1007/3-540-45848-4_14