Algorithms for Generating Minimal Blockers of Perfect Matchings in Bipartite Graphs and Related Problems

摘要

A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, this gives a polynomial delay algorithm for listing the anti-vertices of the perfect matching polytope P(G) = {x ∈ R~E | Hx = e, x ≥ 0}, where H is the incidence matrix of G. We also give similar generation algorithms for other related problems, including d-factors in bipartite graphs, and perfect 2-matchings in general graphs.