Approaches Based on Permutations for Partitioning Sparse Matrices on Multiprocessors

Abstract

This paper introduces new approaches to the data distribution-partition problem for sparse matrices in a multiprocessor environment. In this work, the data partition problem of a sparse matrix is modeled as a Min-Max Problem subject to the uniformity constrain when the goal is to balance the load for both sparse and dense operations. This problem is NP-Complete and two heuristic solutions (ABO and GPB) are proposed. The key of ABO and GPB is to determine the permutation of rows/columns of the input sparse matrix to obtain a sorted matrix with a homogeneous density of nonzero elements. Due to the heuristic nature of the proposed methods their validation is carried out by a comparative study of the parallel efficiency of two types of problems (sparse and mixed) when ABO, GPB, Block, Cyclic and MRD data distributions are applied.

On the exact (whole) diagonalization of large semi-empirical configuration interaction matrices

“…Recently, Tanaka et al [5] developed a spin projected full configuration interaction (FCI) code adapted to parallel computers. Obtaining spin eigenfunctions [6][7][8][9][10][11] and eigenvectors of large matrices [12][13][14] are related topics of current interest. The importance of the diagonalization in the calculation of quantum dots has been reviewed by Reimann and Manninen [9].…”