Drawing directed graphs using one-dimensional optimization

Liran Carmel; David Harel; Yehuda Koren

doi:10.1007/3-540-36151-0_19

Drawing directed graphs using one-dimensional optimization

Liran Carmel^*, David Harel, Yehuda Koren

^*Corresponding author for this work

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

11 Scopus citations

Abstract

We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

Original language	English
Title of host publication	Graph Drawing - 10th International Symposium, GD 2002, Revised Papers
Editors	Michael T. Goodrich, Stephen G. Kobourov
Publisher	Springer Verlag
Pages	193-206
Number of pages	14
ISBN (Print)	3540001581, 9783540001584
DOIs	https://doi.org/10.1007/3-540-36151-0_19
State	Published - 2002
Externally published	Yes
Event	10th International Symposium on Graph Drawing, GD 2002 - Irvine, CA, United States Duration: 26 Aug 2002 → 28 Aug 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2528 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Symposium on Graph Drawing, GD 2002
Country/Territory	United States
City	Irvine, CA
Period	26/08/02 → 28/08/02

Access to Document

10.1007/3-540-36151-0_19

Cite this

Carmel, L., Harel, D., & Koren, Y. (2002). Drawing directed graphs using one-dimensional optimization. In M. T. Goodrich, & S. G. Kobourov (Eds.), Graph Drawing - 10th International Symposium, GD 2002, Revised Papers (pp. 193-206). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2528 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-36151-0_19

Carmel, Liran ; Harel, David ; Koren, Yehuda. / Drawing directed graphs using one-dimensional optimization. Graph Drawing - 10th International Symposium, GD 2002, Revised Papers. editor / Michael T. Goodrich ; Stephen G. Kobourov. Springer Verlag, 2002. pp. 193-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{979b8e09d66a4e91be15eafa200fde3e,

title = "Drawing directed graphs using one-dimensional optimization",

abstract = "We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.",

author = "Liran Carmel and David Harel and Yehuda Koren",

year = "2002",

doi = "10.1007/3-540-36151-0_19",

language = "אנגלית",

isbn = "3540001581",

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

publisher = "Springer Verlag",

pages = "193--206",

editor = "Goodrich, {Michael T.} and Kobourov, {Stephen G.}",

booktitle = "Graph Drawing - 10th International Symposium, GD 2002, Revised Papers",

address = "גרמניה",

note = "10th International Symposium on Graph Drawing, GD 2002 ; Conference date: 26-08-2002 Through 28-08-2002",

}

Carmel, L, Harel, D & Koren, Y 2002, Drawing directed graphs using one-dimensional optimization. in MT Goodrich & SG Kobourov (eds), Graph Drawing - 10th International Symposium, GD 2002, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2528 LNCS, Springer Verlag, pp. 193-206, 10th International Symposium on Graph Drawing, GD 2002, Irvine, CA, United States, 26/08/02. https://doi.org/10.1007/3-540-36151-0_19

Drawing directed graphs using one-dimensional optimization. / Carmel, Liran; Harel, David; Koren, Yehuda.
Graph Drawing - 10th International Symposium, GD 2002, Revised Papers. ed. / Michael T. Goodrich; Stephen G. Kobourov. Springer Verlag, 2002. p. 193-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2528 LNCS).

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

TY - GEN

T1 - Drawing directed graphs using one-dimensional optimization

AU - Carmel, Liran

AU - Harel, David

AU - Koren, Yehuda

PY - 2002

Y1 - 2002

N2 - We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

AB - We present an algorithm for drawing directed graphs, which is based on rapidly solving a unique one-dimensional optimization problem for each of the axes. The algorithm results in a clear description of the hierarchy structure of the graph. Nodes are not restricted to lie on fixed horizontal layers, resulting in layouts that convey the symmetries of the graph very naturally. The algorithm can be applied without change to cyclic or acyclic digraphs, and even to graphs containing both directed and undirected edges. We also derive a hierarchy index from the input digraph, which quantitatively measures its amount of hierarchy.

UR - http://www.scopus.com/inward/record.url?scp=84867457323&partnerID=8YFLogxK

U2 - 10.1007/3-540-36151-0_19

DO - 10.1007/3-540-36151-0_19

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84867457323

SN - 3540001581

SN - 9783540001584

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

SP - 193

EP - 206

BT - Graph Drawing - 10th International Symposium, GD 2002, Revised Papers

A2 - Goodrich, Michael T.

A2 - Kobourov, Stephen G.

PB - Springer Verlag

T2 - 10th International Symposium on Graph Drawing, GD 2002

Y2 - 26 August 2002 through 28 August 2002

ER -

Carmel L, Harel D, Koren Y. Drawing directed graphs using one-dimensional optimization. In Goodrich MT, Kobourov SG, editors, Graph Drawing - 10th International Symposium, GD 2002, Revised Papers. Springer Verlag. 2002. p. 193-206. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-36151-0_19

Drawing directed graphs using one-dimensional optimization

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this