ACE: A fast multiscale eigenvectors computation for drawing huge graphs

Yehuda Koren; L. Carmel; D. Harel

doi:10.1109/INFVIS.2002.1173159

ACE: A fast multiscale eigenvectors computation for drawing huge graphs

Yehuda Koren, L. Carmel, D. Harel

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

102 Scopus citations

Abstract

We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is expressed as a generalized eigenvalue problem, which is rapidly solved using a novel algebraic multigrid technique. The same generalized eigenvalue problem seems to come up also in other fields, hence ACE appears to be applicable outside of graph drawing too.

Original language	English
Title of host publication	IEEE Symposium on Information Visualization 2002, INFOVIS 2002
Editors	Keith Andrews, Pak Chung Wong
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	137-144
Number of pages	8
ISBN (Electronic)	076951751X
DOIs	https://doi.org/10.1109/INFVIS.2002.1173159
State	Published - 2002
Externally published	Yes
Event	IEEE Symposium on Information Visualization, INFOVIS 2002 - Boston, United States Duration: 28 Oct 2002 → 29 Oct 2002

Publication series

Name	Proceedings - IEEE Symposium on Information Visualization, INFO VIS
Volume	2002-January
ISSN (Print)	1522-404X

Conference

Conference	IEEE Symposium on Information Visualization, INFOVIS 2002
Country/Territory	United States
City	Boston
Period	28/10/02 → 29/10/02

Bibliographical note

Publisher Copyright:
© 2002 IEEE.

Keywords

Clustering algorithms
Computer science
Data visualization
Eigenvalues and eigenfunctions
Image segmentation
Joining processes
Laplace equations
Mathematics
Minimization methods
Partitioning algorithms

Access to Document

10.1109/INFVIS.2002.1173159

Cite this

Koren, Y., Carmel, L., & Harel, D. (2002). ACE: A fast multiscale eigenvectors computation for drawing huge graphs. In K. Andrews, & P. C. Wong (Eds.), IEEE Symposium on Information Visualization 2002, INFOVIS 2002 (pp. 137-144). Article 1173159 (Proceedings - IEEE Symposium on Information Visualization, INFO VIS; Vol. 2002-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/INFVIS.2002.1173159

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abstract = "We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is expressed as a generalized eigenvalue problem, which is rapidly solved using a novel algebraic multigrid technique. The same generalized eigenvalue problem seems to come up also in other fields, hence ACE appears to be applicable outside of graph drawing too.",

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Koren, Y, Carmel, L & Harel, D 2002, ACE: A fast multiscale eigenvectors computation for drawing huge graphs. in K Andrews & PC Wong (eds), IEEE Symposium on Information Visualization 2002, INFOVIS 2002., 1173159, Proceedings - IEEE Symposium on Information Visualization, INFO VIS, vol. 2002-January, Institute of Electrical and Electronics Engineers Inc., pp. 137-144, IEEE Symposium on Information Visualization, INFOVIS 2002, Boston, United States, 28/10/02. https://doi.org/10.1109/INFVIS.2002.1173159

ACE: A fast multiscale eigenvectors computation for drawing huge graphs. / Koren, Yehuda; Carmel, L.; Harel, D.
IEEE Symposium on Information Visualization 2002, INFOVIS 2002. ed. / Keith Andrews; Pak Chung Wong. Institute of Electrical and Electronics Engineers Inc., 2002. p. 137-144 1173159 (Proceedings - IEEE Symposium on Information Visualization, INFO VIS; Vol. 2002-January).

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

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KW - Eigenvalues and eigenfunctions

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KW - Joining processes

KW - Laplace equations

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KW - Minimization methods

KW - Partitioning algorithms

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Koren Y, Carmel L, Harel D. ACE: A fast multiscale eigenvectors computation for drawing huge graphs. In Andrews K, Wong PC, editors, IEEE Symposium on Information Visualization 2002, INFOVIS 2002. Institute of Electrical and Electronics Engineers Inc. 2002. p. 137-144. 1173159. (Proceedings - IEEE Symposium on Information Visualization, INFO VIS). doi: 10.1109/INFVIS.2002.1173159

ACE: A fast multiscale eigenvectors computation for drawing huge graphs

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