Communication results for parallel sparse Cholesky factorization on a hypercube

We consider the problem of reducing data traffic among processor nodes during the parallel factorization of a sparse matrix on a hypercube multiprocessor. A task assignment strategy based on the structure of an elimination tree is presented. This assignment is aimed at achieving load balancing among the processors and also reducing the amount of processor-to-processor data communication. An analysis of regular grid problems is presented, providing a bound on communication volume generated by the new strategy, and showing that the allocation scheme is optimal in the asymptotic sense. Some experimental results on the performance of this scheme are presented.