Drawing huge graphs by algebraic multigrid optimization

Yehuda Koren, Liran Carmel, David Harel

Research output: Contribution to journalArticlepeer-review

51 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 a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, 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 solved rapidly 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 graph drawing too.

Original languageAmerican English
Pages (from-to)645-673
Number of pages29
JournalMultiscale Modeling and Simulation
Issue number4
StatePublished - 2003
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2003 Society for Industrial and Applied Mathematics.


  • Algebraic multigrid
  • Fiedler vector
  • Force directed layout
  • Generalized eigenvalue problem
  • Graph drawing
  • Multiscale/multilevel optimization
  • The Hall energy


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