Monotone drawings of graphs with fixed embedding

Patrizio Angelini, Walter Didimo, Stephen G Kobourov, Tamara McHedlidze, Vincenzo Roselli, Antonios Symvonis, Stephen Wismath

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

5 Citations (Scopus)

Abstract

A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n - 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages379-390
Number of pages12
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

Monotone
Polynomials
Graph in graph theory
Planar graph
Linear Time
Embedded Graph
Drawing
Straight Line
Path
Polynomial
Necessary

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Angelini, P., Didimo, W., Kobourov, S. G., McHedlidze, T., Roselli, V., Symvonis, A., & Wismath, S. (2012). Monotone drawings of graphs with fixed embedding. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7034 LNCS, pp. 379-390). (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_36

Monotone drawings of graphs with fixed embedding. / Angelini, Patrizio; Didimo, Walter; Kobourov, Stephen G; McHedlidze, Tamara; Roselli, Vincenzo; Symvonis, Antonios; Wismath, Stephen.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. p. 379-390 (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

Angelini, P, Didimo, W, Kobourov, SG, McHedlidze, T, Roselli, V, Symvonis, A & Wismath, S 2012, Monotone drawings of graphs with fixed embedding. 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. 379-390, 19th International Symposium on Graph Drawing, GD 2011, Eindhoven, Netherlands, 9/21/11. https://doi.org/10.1007/978-3-642-25878-7_36
Angelini P, Didimo W, Kobourov SG, McHedlidze T, Roselli V, Symvonis A et al. Monotone drawings of graphs with fixed embedding. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS. 2012. p. 379-390. (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_36
Angelini, Patrizio ; Didimo, Walter ; Kobourov, Stephen G ; McHedlidze, Tamara ; Roselli, Vincenzo ; Symvonis, Antonios ; Wismath, Stephen. / Monotone drawings of graphs with fixed embedding. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7034 LNCS 2012. pp. 379-390 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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