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Researchers achieve ‘absurdly fast’ algorithm for network flow

quantamagazine.org

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Re: Researchers achieve ‘absurdly fast’ algorithm for network flow

#4
> Maximum Flow and Minimum-Cost Flow in Almost-Linear Time

> We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m^(1+o(1)) time. Our algorithm builds the flow through a sequence of m^(1+o(1)) approximate undirected minimum-ratio cycles, each of which is computed and processed in amortized m^o(1) time using a new dynamic graph data structure.

^ Our framework extends to algorithms running in m^(1+o(1)) time for computing flows that minimize general edge-separable convex functions to high accuracy. This gives almost-linear time algorithms for several problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and p-norm isotonic regression on arbitrary directed acyclic graphs.

https://arxiv.org/abs/2203.00671

Re: Researchers achieve ‘absurdly fast’ algorithm for network flow

#7
post #3

It ALSO does minimum cost? Is this academically published? Is this newer than the various links that date to 2010?

The link to the paper is n the 1st paragraph: https://arxiv.org/abs/2203.00671

And the PDF here: https://arxiv.org/pdf/2203.00671v2.pdf
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