Minimum communication cost reordering for parallel sparse Cholesky factorization - Lin, Wen-Yang; Chen, Chuen-Liang (Parallel computing, 1999)
In this paper, we consider the problem of reducing the communication cost for the parallel factorization of a sparse symmetric positive definite matrix on a distributed-memory multiprocessor. We define a parallel communication cost function and show that, with a contrived example, simply minimizing the height of the elimination tree is ineffective for exploiting minimum communication cost and the discrepancy may grow infinitely. We propose an algorithm to find an ordering such that the communication cost to complete the parallel Cholesky factorization is minimum among all equivalent reorderings. Our algorithm consumes O( nlog n+ m) in time, where n is the number of nodes and m the sum of all maximal clique sizes in the filled graph.