Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back

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.


Published in:
2013 IEEE 54th Annual Symposium on Foundations of Computer Science (Focs), 253-262
Presented at:
IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS)
Year:
2013
Publisher:
New York, IEEE
ISBN:
978-0-7695-5135-7
Keywords:
Laboratories:




 Record created 2014-06-02, last modified 2018-09-13


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