Algorithm for generating a step matrix by permutation

Abstract

With an efficient algorithm it can be tested whether an n-dimensional matrix B can be reduced by a permutation. The optimal step matrix, which can be obtained by a permutation, is calculated. The algorithm needs 0(n 2 -n) operations in the case of an array reprsentation of B. If B is a Sparse matrix with m non-zero offdiagonal elements, the cost is of the order 0(max(m, nlog2(n))). Storage for 4 integer arrays of length n is necessary.