A Weighted Linear Matroid Parity Algorithm

Weighted Linear Matroid Parity

Shortest Disjoint S-Paths Via Weighted Linear Matroid Parity

Mader’s disjoint S-paths problem unifies two generalizations of bipartite matching: (a) nonbipartite matching and (b) disjoint s–t paths. Lovász (1980, 1981) first proposed an efficient algorithm for this problem via a reduction to matroid matching, which also unifies two generalizations of bipartite matching: (a) non-bipartite matching and (c) matroid intersection. While the weighted versions ...

The linear delta-matroid parity problem

This paper addresses a generalization of the matroid parity problem to delta-matroids. We give a minimax relation, as well as an efficient algorithm, for linearly represented deltamatroids. These are natural extensions of the minimax theorem of Lovász and the augmenting path algorithm of Gabow and Stallmann for the linear matroid parity problem. r 2003 Elsevier Science (USA). All rights reserved.

A Algebraic Algorithms for Linear Matroid Parity Problems

We present fast and simple algebraic algorithms for the linear matroid parity problem and its applications. For the linear matroid parity problem, we obtain a simple randomized algorithm with running time O(mrω−1) where m and r are the number of columns and the number of rows and ω ≈ 2.3727 is the matrix multiplication exponent. This improves the O(mrω)-time algorithm by Gabow and Stallmann, an...

A Fast, Simpler Algorithm for the Matroid Parity Problem

Consider a matrix with m rows and n pairs of columns. The linear matroid parity problem (LMPP) is to determine a maximum number of pairs of columns that are linearly independent. We show how to solve the linear matroid parity problem as a sequence of matroid intersection problems. The algorithm runs in O(mn). Our algorithm is comparable to the best running time for the LMPP, and is far simpler ...