Matrix decomposition on the star graph

Abstract

We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N/sup 3//n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N/spl ges/(n-1)!. The incurred communication time is better than the best known results for the hypercube, O(Nlogn!), and the mesh, O(N/spl radic/n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.