TY - CPAPER
DO - 10.1109/Focs.2013.35
AB - We present an O(m^10/7) = O(m^1.43)-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing O(m min{m^1/2, n^2/3}) running time bound due to Even and Tarjan [16]. By well-known reductions, this also establishes an O(m^10/7)-time algorithm for the maximum-cardinality bipartite matching problem. That, in turn, gives an improvement over the celebrated O(mn^1/2) running time bound of Hopcroft and Karp [25] whenever the input graph is sufficiently sparse. At a very high level, our results stem from acquiring a deeper understanding of interior-point methods - a powerful tool in convex optimization - in the context of flow problems, as well as, utilizing certain interplay between maximum flows and bipartite matchings.
T1 - Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back
DA - 2013
AU - Madry, Aleksander
JF - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (Focs)
SP - 253-262
EP - 253-262
PB - IEEE
PP - New York
ID - 199296
KW - maximum flow problem
KW - minimum s-t cut problem
KW - bipartite matchings
KW - electrical flows
KW - interior-point methods
KW - central path
KW - Laplacian linear systems
SN - 978-0-7695-5135-7
ER -