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Spectral partitioning works: planar graphs and finite element meshes
Abstract
Spectral partitioning methods use the Fiedler vector-the eigenvector of the second-smallest eigenvalue of the Laplacian matrix-to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree planar graphs and finite element meshes-the classes of graphs to which they are usually applied. While active spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O(/spl radic/n) for bounded-degree planar graphs and two-dimensional meshes and O(n/sup 1/d/) for well-shaped d-dimensional meshes. The heart of our analysis is an upper bound on the second-smallest eigenvalues of the Laplacian matrices of these graphs: we prove a bound of O(1/n) for bounded-degree planar graphs and O(1/n/sup 2/d/) for well-shaped d-dimensional meshes.
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Cites
Chung, F. (1996) · CBMS Regional Conference Series in Mathematics · doi:10.1090/cbms/092 · Cited by 5,524
Computer Simulation Using Particles
Hockney, R. W., & Eastwood, J. W. (1988) · Institute of Physics eBooks · doi:10.1887/0852743920 · Cited by 5,441
A fast algorithm for particle simulations
Greengard, L., & Rokhlin, V (1987) · Journal of Computational Physics · doi:10.1016/0021-9991(87)90140-9 · Cited by 4,868
Algebraic connectivity of graphs
Fiedler, M. (1973) · Czechoslovak Mathematical Journal · doi:10.21136/cmj.1973.101168 · Cited by 3,977
An analysis of the finite element method
(1980) · Advances in Water Resources · doi:10.1016/0309-1708(80)90069-x · Cited by 3,466
Sphere Packings, Lattices and Groups.
Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A. (1989) · The American Mathematical Monthly · doi:10.2307/2323992 · Cited by 3,377
Biggs, N. (1974) · doi:10.1017/cbo9780511608704 · Cited by 2,940
Spectra of graphs : theory and application
Cvetković, D., Doob, M., & Sachs, H. (1995) · Cited by 1,825
Algorithms in Combinatorial Geometry.
Goodman, J. E., & Edelsbrunner, H. (1989) · The American Mathematical Monthly · doi:10.2307/2325168 · Cited by 1,788
Numerical solution of partial differential equations by the finite element method
(1988) · Choice Reviews Online · doi:10.5860/choice.26-0972 · Cited by 1,783
Cited by
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
A tutorial on spectral clustering
von Luxburg, U. (2007) · Statistics and Computing · doi:10.1007/s11222-007-9033-z · Cited by 10,349
Schaeffer, S. E. (2007) · Computer Science Review · doi:10.1016/j.cosrev.2007.05.001 · Cited by 1,639
Mechanism Design via Differential Privacy
McSherry, F., & Talwar, K. (2007) · 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) · doi:10.1109/focs.2007.66 · Cited by 1,371
Local Graph Partitioning using PageRank Vectors
Andersen, R., Chung, F., & Lang, K. (2006) · 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) · doi:10.1109/focs.2006.44 · Cited by 967
Metadata
- Authors
- Spielman, D. A., & Teng, S.-H.
- Venue
- Proceedings of 37th Conference on Foundations of Computer Science
- Publisher
- IEEE
- Published
- 1996
- Pages
- 96-105
- OpenAlex
- W2067976091
- Cited by
- 393
- References
- 44
- FWCI
- 6.97
- Type
- conference paper
- Language
- en
- Open access
- closed
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