Proportional contact representations of planar graphs

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

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

9 Citations (Scopus)

Abstract

We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages26-38
Number of pages13
Volume7034 LNCS
DOIs
StatePublished - 2012
Event19th International Symposium on Graph Drawing, GD 2011 - Eindhoven, Netherlands
Duration: Sep 21 2011Sep 23 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7034 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other19th International Symposium on Graph Drawing, GD 2011
CountryNetherlands
CityEindhoven
Period9/21/119/23/11

Fingerprint

Point contacts
Planar graph
Directly proportional
Contact
Polygon
Outerplanar Graph
Simple Polygon
Adjacency
Partial
Optimization
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Alam, M. J., Biedl, T., Felsner, S., Kaufmann, M., & Kobourov, S. G. (2012). Proportional contact representations of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7034 LNCS, pp. 26-38). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7034 LNCS). https://doi.org/10.1007/978-3-642-25878-7_4

Proportional contact representations of planar graphs. / Alam, Muhammad Jawaherul; Biedl, Therese; Felsner, Stefan; Kaufmann, Michael; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. p. 26-38 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7034 LNCS).

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

Alam, MJ, Biedl, T, Felsner, S, Kaufmann, M & Kobourov, SG 2012, Proportional contact representations of planar graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7034 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7034 LNCS, pp. 26-38, 19th International Symposium on Graph Drawing, GD 2011, Eindhoven, Netherlands, 9/21/11. https://doi.org/10.1007/978-3-642-25878-7_4
Alam MJ, Biedl T, Felsner S, Kaufmann M, Kobourov SG. Proportional contact representations of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS. 2012. p. 26-38. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25878-7_4
Alam, Muhammad Jawaherul ; Biedl, Therese ; Felsner, Stefan ; Kaufmann, Michael ; Kobourov, Stephen G. / Proportional contact representations of planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. pp. 26-38 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{c2760644554a47229e4d28f59e0964a6,
title = "Proportional contact representations of planar graphs",
abstract = "We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.",
author = "Alam, {Muhammad Jawaherul} and Therese Biedl and Stefan Felsner and Michael Kaufmann and Kobourov, {Stephen G}",
year = "2012",
doi = "10.1007/978-3-642-25878-7_4",
language = "English (US)",
isbn = "9783642258770",
volume = "7034 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "26--38",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - Proportional contact representations of planar graphs

AU - Alam, Muhammad Jawaherul

AU - Biedl, Therese

AU - Felsner, Stefan

AU - Kaufmann, Michael

AU - Kobourov, Stephen G

PY - 2012

Y1 - 2012

N2 - We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.

AB - We study contact representations for planar graphs, with vertices represented by simple polygons and adjacencies represented by point-contacts or side-contacts between the corresponding polygons. Specifically, we consider proportional contact representations, where pre-specified vertex weights must be represented by the areas of the corresponding polygons. Several natural optimization goals for such representations include minimizing the complexity of the polygons, the cartographic error, and the unused area. We describe constructive algorithms for proportional contact representations with optimal complexity for general planar graphs and planar 2-segment graphs, which include maximal outerplanar graphs and partial 2-trees.

UR - http://www.scopus.com/inward/record.url?scp=84455182319&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84455182319&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25878-7_4

DO - 10.1007/978-3-642-25878-7_4

M3 - Conference contribution

SN - 9783642258770

VL - 7034 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 26

EP - 38

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -