ACE: A fast multiscale eigenvectors computation for drawing huge graphs

Yehuda Koren, L. Carmel, D. Harel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

100 Scopus citations


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 languageAmerican English
Title of host publicationIEEE Symposium on Information Visualization 2002, INFOVIS 2002
EditorsKeith Andrews, Pak Chung Wong
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Electronic)076951751X
StatePublished - 2002
Externally publishedYes
EventIEEE Symposium on Information Visualization, INFOVIS 2002 - Boston, United States
Duration: 28 Oct 200229 Oct 2002

Publication series

NameProceedings - IEEE Symposium on Information Visualization, INFO VIS
ISSN (Print)1522-404X


ConferenceIEEE Symposium on Information Visualization, INFOVIS 2002
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© 2002 IEEE.


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


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