Computing DM-decomposition of a partitioned matrix with rank-1 blocks

TL;DR

This paper presents a polynomial time algorithm for computing a Dulmage-Mendelsohn-type decomposition of matrices partitioned into submatrices of rank at most one, facilitating analysis of such structured matrices.

Contribution

The paper introduces the first polynomial time algorithm for DM-decomposition of partitioned matrices with rank-1 blocks, extending existing decomposition techniques.

Findings

Algorithm operates in polynomial time

Effective for matrices with rank-1 block structures

Enables new analysis methods for structured matrices

Abstract

In this paper, we develop a polynomial time algorithm to compute a Dulmage-Mendelsohn-type decomposition of a matrix partitioned into submatrices of rank at most $1$.