A graph based method for generating the fiedler vector of irregular problems
In this paper we present new algorithms for spectral graph partitioning. Previously, the best partitioning methods were based on a combination of Combinatorial algorithms and application of the Lanczos method when the graph allows this method to be cheap enough. Our new algorithms are purely spectral. They calculate the Fiedler vector of the original graph and use the information about the problem in the form of a preconditioner for the graph Laplacian. In addition, we use a favorable subspace for starting the Davidson algorithm and reordering of variables for locality of memory references.
Unable to display preview. Download preview PDF.
- 1.S. Barnard and H. Simon. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. In Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, Norfolk, Virginia, 1993. SIAM, SIAM.Google Scholar
- 2.L. Borges and S. Oliveira. A parallel Davidson-type algorithm for several eigenvalues. Journal of Computational Physics, (144):763–770, August 1998.Google Scholar
- 8.M. Holzrichter and S. Oliveira. New spectral graph partitioning algorithms. submitted.Google Scholar
- 9.M. Holzrichter and S. Oliveira. New graph partitioning algorithms. 1998. The University of Iowa TR-120.Google Scholar
- 10.G. Karypis and V. Kumar. Multilevel k-way partitioning scheme for irregular garphs. to appear in the Journal of Parallel and Distributed Computing.Google Scholar
- 14.S. Oliveira. A convergence proof of an iterative subspace method for eigenvalues problem. In F. Cucker and M. Shub, editors, Foundations of Computational Mathematics Selected Papers, pages 316–325. Springer, January 1997.Google Scholar
- 17.D. Spielman and S. H. Teng. Spectral partitioning works: planar graphs and finite element meshes. In 37th Annual Symposium Foundations of Computer Science, Burlington, Vermont, October 1996. IEEE, IEEE Press.Google Scholar