Computing covers from matchings with permutations

We present a matrix permutation algorithm for computing a minimal vertex cover from a maximal matching in a bipartite graph. Our algorithm is linear time and linear space, and provides an interesting perspective on a well known problem. Unlike most algorithms, it does not use the concept of alternating paths, and it is formulated entirely in terms of combinatorial operations on a binary matrix. The algorithm relies on permutations of rows and columns of a 0-1 matrix which encodes a bipartite graph together with its maximal matching. This problem has many important applications such as network switches which essentially compute maximal matchings between their incoming and outgoing ports.