Sparse matrix permutations to a block triangular form in a distributed environment

Arranging the sparse circuit matrix into a diagonal block upper triangular form is the first step of the KLU algorithm. This paper presents the two steps of the parallel algorithm, running in a distributed environment, that performs unsymmetric and symmetric permutations of the matrix's rows. First, using the [Duff] maximum transversal algorithm and performing asymmetrical permutations, the matrix is shaped to achieve a zero free diagonal. Then, searching the strongly connected components of the associated matrix's graph, and performing symmetric permutation, the sparse matrix is shaped in a diagonal block upper triangular form. Both algorithm and architecture are presented.