Minimizing maximum weight of subsets of a maximum matching in a bipartite graph

A scaling algorithm for maximum weight matching in bipartite graphs

Given a weighted bipartite graph, the maximum weight matching (MWM) problem is to find a set of vertex-disjoint edges with maximum weight. We present a new scaling algorithm that runs in O(m √ n logN) time, when the weights are integers within the range of [0, N ]. The result improves the previous bounds of O(Nm √ n) by Gabow and O(m √ n log (nN)) by Gabow and Tarjan over 20 years ago. Our impr...

The Maximum Number of Edges in a Strongly Multiplicative Graph

Maximum weight bipartite matching in matrix multiplication time

In this paper we consider the problem of finding maximum weight matchings in bipartite graphs with nonnegative integer weights. The presented algorithm for this problemworks in Õ(Wnω)1 time, whereω is thematrixmultiplication exponent, andW is the highest edge weight in the graph. As a consequence of this result we obtain Õ(Wn) time algorithms for computing: minimum weight bipartite vertex cover...

Loopy Belief Propagation for Bipartite Maximum Weight b-Matching

We formulate the weighted b-matching objective function as a probability distribution function and prove that belief propagation (BP) on its graphical model converges to the optimum. Standard BP on our graphical model cannot be computed in polynomial time, but we introduce an algebraic method to circumvent the combinatorial message updates. Empirically, the resulting algorithm is on average fas...

Maximum semi-matching problem in bipartite graphs

An (f, g)-semi-matching in a bipartite graph G = (U ∪V,E) is a set of edges M ⊆ E such that each vertex u ∈ U is incident with at most f(u) edges of M , and each vertex v ∈ V is incident with at most g(v) edges of M . In this paper we give an algorithm that for a graph with n vertices and m edges, n ≤ m, constructs a maximum (f, g)semi-matching in running time O(m ·min( √∑ u∈U f(u), √∑ v∈V g(v)...