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 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages281-291
Number of pages11
Volume7074 LNCS
DOIs
StatePublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Graph Representation
Linear-time Algorithm
Polygon
Directly proportional
Contact
Planar graph
Simple Polygon
Adjacency
Rectangle
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7074 LNCS, 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

Linear-time algorithms for hole-free rectilinear proportional contact graph representations. / Alam, Muhammad Jawaherul; Biedl, Therese; Felsner, Stefan; Gerasch, Andreas; Kaufmann, Michael; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7074 LNCS 2011. p. 281-291 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS).

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

Alam, MJ, Biedl, T, Felsner, S, Gerasch, A, Kaufmann, M & Kobourov, SG 2011, Linear-time algorithms for hole-free rectilinear proportional contact graph representations. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7074 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7074 LNCS, pp. 281-291, 22nd International Symposium on Algorithms and Computation, ISAAC 2011, Yokohama, Japan, 12/5/11. https://doi.org/10.1007/978-3-642-25591-5_30
Alam MJ, Biedl T, Felsner S, Gerasch A, Kaufmann M, Kobourov SG. Linear-time algorithms for hole-free rectilinear proportional contact graph representations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7074 LNCS. 2011. p. 281-291. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25591-5_30
Alam, Muhammad Jawaherul ; Biedl, Therese ; Felsner, Stefan ; Gerasch, Andreas ; Kaufmann, Michael ; Kobourov, Stephen G. / Linear-time algorithms for hole-free rectilinear proportional contact graph representations. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7074 LNCS 2011. pp. 281-291 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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