Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back
Abstract
We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$time algorithm for the maximum st flow and the minimum st cut problems in directed graphs with unit capacities. This is the first improvement over the sparsegraph case of the longstanding $O(m \min(\sqrt{m},n^{2/3}))$ time bound due to Even and Tarjan [EvenT75]. By wellknown reductions, this also establishes an $\tilde{O}(m^{10/7})$time algorithm for the maximumcardinality bipartite matching problem. That, in turn, gives an improvement over the celebrated celebrated $O(m \sqrt{n})$ time bound of Hopcroft and Karp [HK73] whenever the input graph is sufficiently sparse.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 arXiv:
 arXiv:1307.2205
 Bibcode:
 2013arXiv1307.2205M
 Keywords:

 Computer Science  Data Structures and Algorithms