For the first time there is an almost-linear-time construction of an O(mo(1))-competitive oblivious routing scheme. No previous such algorithm ran in time better than ( e mn). By reducing the running time to almost-linear, our work provides a powerful new primitive for constructing very fast

graph algorithms.

An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations

In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.

Maxflow problems are like airline scheduling.

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