Compressed Graphs and the Minimum Degree Algorithm

Abstract

The minimum degree algorithm is well known and widely used to find a permutation matrix P such that a sparse symmetric positive definite matrix A can be factored as $PAP^T = LL^T $ to yield a lower triangular matrix L with relatively few nonzero entries. In this paper we show that by compressing the graph of A, when possible, the run time of the minimum degree algorithm can be significantly reduced. Some empirical results for a collection of test matrices are presented.