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 diierent partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing ll-in in matrix factorizations and load-balancing 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.