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An almostlineartime algorithm for approximate max flow in undirected graphs, and its multicommodity generalizations
"... In this paper we present an almost linear time algorithm for solving approximate maximum flow in undirected graphs. In particular, given a graph with m edges we show how to produce a 1−ε approximate maximum flow in time O(m 1+o(1) · ε −2). Furthermore, we present this algorithm as part of a general ..."
Abstract

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In this paper we present an almost linear time algorithm for solving approximate maximum flow in undirected graphs. In particular, given a graph with m edges we show how to produce a 1−ε approximate maximum flow in time O(m 1+o(1) · ε −2). Furthermore, we present this algorithm as part of a general framework that also allows us to achieve a running time of O(m 1+o(1) ε −2 k 2) for the maximum concurrent kcommodity flow problem, the first such algorithm with an almost linear dependence on m. We also note that independently Jonah Sherman has produced an almost linear time algorithm for maximum flow and we thank him for coordinating submissions.