# Algebraic Algorithms for B-Matching, Shortest Undirected Paths, and F-Factors

@article{Gabow2013AlgebraicAF, title={Algebraic Algorithms for B-Matching, Shortest Undirected Paths, and F-Factors}, author={Harold N. Gabow and Piotr Sankowski}, journal={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, year={2013}, pages={137-146} }

Let G = (V, E) be a graph with f : V → Z+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is O(f(V )ω). More generally for graphs with integral edge weights of maximum absolute value W we find a maximum weight f-factor in time Õ(Wf(V )ω). (The algorithms are correct with high probability and can be made Las Vegas.) We also present three specializations of these algorithms: For maximum weight perfect f-matching the…

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