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.
Bibliographical notePublisher 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