Abstract
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 ∈ ℝE | 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.
This research was supported by the National Science Foundation (Grant IIS-0118635). The third author is also grateful for the partial support by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science.
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Boros, E., Elbassioni, K., Gurvich, V. (2004). Algorithms for Generating Minimal Blockers of Perfect Matchings in Bipartite Graphs and Related Problems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_13
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DOI: https://doi.org/10.1007/978-3-540-30140-0_13
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