Monotone drawings of graphs with fixed embedding

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

doi:10.1007/978-3-642-25878-7_36

Monotone drawings of graphs with fixed embedding

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

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

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 language	English (US)
Title of host publication	Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers
Pages	379-390
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-25878-7_36
State	Published - 2012
Event	19th International Symposium on Graph Drawing, GD 2011 - Eindhoven, Netherlands Duration: Sep 21 2011 → Sep 23 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7034 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	19th International Symposium on Graph Drawing, GD 2011
Country	Netherlands
City	Eindhoven
Period	9/21/11 → 9/23/11

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-25878-7_36

Fingerprint Dive into the research topics of 'Monotone drawings of graphs with fixed embedding'. Together they form a unique fingerprint.

Cite this

Angelini, P., Didimo, W., Kobourov, S., McHedlidze, T., Roselli, V., Symvonis, A., & Wismath, S. (2012). Monotone drawings of graphs with fixed embedding. In Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers (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; McHedlidze, Tamara; Roselli, Vincenzo; Symvonis, Antonios; Wismath, Stephen.

Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers. 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 proceeding › Conference contribution

Angelini, P, Didimo, W, Kobourov, S, McHedlidze, T, Roselli, V, Symvonis, A & Wismath, S 2012, Monotone drawings of graphs with fixed embedding. in Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers. 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 S, McHedlidze T, Roselli V, Symvonis A et al. Monotone drawings of graphs with fixed embedding. In Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers. 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 ; McHedlidze, Tamara ; Roselli, Vincenzo ; Symvonis, Antonios ; Wismath, Stephen. / Monotone drawings of graphs with fixed embedding. Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers. 2012. pp. 379-390 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{c50b79640d724493bd899a0e7d2a0989,

title = "Monotone drawings of graphs with fixed embedding",

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.",

author = "Patrizio Angelini and Walter Didimo and Stephen Kobourov and Tamara McHedlidze and Vincenzo Roselli and Antonios Symvonis and Stephen Wismath",

year = "2012",

doi = "10.1007/978-3-642-25878-7_36",

language = "English (US)",

isbn = "9783642258770",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "379--390",

booktitle = "Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers",

}

TY - GEN

T1 - Monotone drawings of graphs with fixed embedding

AU - Angelini, Patrizio

AU - Didimo, Walter

AU - Kobourov, Stephen

AU - McHedlidze, Tamara

AU - Roselli, Vincenzo

AU - Symvonis, Antonios

AU - Wismath, Stephen

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84455209585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84455209585&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25878-7_36

DO - 10.1007/978-3-642-25878-7_36

M3 - Conference contribution

AN - SCOPUS:84455209585

SN - 9783642258770

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

SP - 379

EP - 390

BT - Graph Drawing - 19th International Symposium, GD 2011, Revised Selected Papers

T2 - 19th International Symposium on Graph Drawing, GD 2011

Y2 - 21 September 2011 through 23 September 2011

ER -