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A Graph Based Method for Generating the Fiedler Vector of Irregular Problems
 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1999
"... 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 spectra ..."
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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.
A Graph Based Davidson Algorithm for the Graph Partitioning Problem
"... The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fillin in matrix factorizations and loadbalancing for parallel algorithms. Spectral gr ..."
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Cited by 1 (1 self)
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The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fillin in matrix factorizations and loadbalancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the eigenvector associated with the second smallest eigenvalue of a matrix called the graph Laplacian. The focus of this paper is the use graph theory to compute this eigenvector more quickly. Keywords: Graph Partitioning Algorithms, Spectral Algorithms, Fiedler Vector, Eigenvalue solvers 1. Introduction The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized arises in many contexts. For example, the nested dissection algorithm [13] uses a solution to the graph partitioning problem to find permutations of sparse matrices which reduce fillin. Graph partitioning has been ...