Linear-time algorithms for hole-free rectilinear proportional contact graph representations

Muhammad Jawaherul Alam, Therese Biedl, Stefan Felsner, Andreas Gerasch, Michael Kaufmann, Stephen G. Kobourov

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

8 Scopus citations

Abstract

In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representations that use rectilinear polygons without wasted areas (white space). In this setting, the best known algorithm for proportional contact representation of a maximal planar graph uses 12-sided rectilinear polygons and takes O(nlogn) time. We describe a new algorithm that guarantees 10-sided rectilinear polygons and runs in O(n) time. We also describe a linear-time algorithm for proportional contact representation of planar 3-trees with 8-sided rectilinear polygons and show that this is optimal, as there exist planar 3-trees that require 8-sided polygons. Finally, we show that a maximal outer-planar graph admits a proportional contact representation using rectilinear polygons with 6 sides when the outer-boundary is a rectangle and with 4 sides otherwise.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
Pages281-291
Number of pages11
DOIs
StatePublished - Dec 26 2011
Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
Duration: Dec 5 2011Dec 8 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7074 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd International Symposium on Algorithms and Computation, ISAAC 2011
CountryJapan
CityYokohama
Period12/5/1112/8/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Alam, M. J., Biedl, T., Felsner, S., Gerasch, A., Kaufmann, M., & Kobourov, S. G. (2011). Linear-time algorithms for hole-free rectilinear proportional contact graph representations. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings (pp. 281-291). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_30