• DOI:10.1109/FOCS.2013.23
• Corpus ID: 10015778

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}
}

• H. Gabow, P. Sankowski
• Published 24 April 2013
• Mathematics, Computer Science
• 2013 IEEE 54th Annual Symposium on Foundations of Computer Science

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 algorithm is considerably simpler (and almost identical to its special case of ordinary weighted matching). For the single-source shortestpath problem in undirected graphs with conservative edge weights, we define a generalization of the shortest-path tree, and we compute it in ̃Õ(Wnω) time. For bipartite graphs, we improve the known complexity bounds for vertex-capacitated max-flow and min-cost max-flow on a subclass of graphs.