Faster Algorithms for Unit Maximum Flow

Abstract: The maximum flow problem is one of the most well-studied problems in combinatorial optimization, encompassing a broad range of cut, matching, and scheduling problems. Here we present a recent line of work obtaining provably faster algorithms for solving the maximum flow problem using interior point methods. In particular, we show how to solve the maximum flow problem in m-edge unit capacity graphs in time almost $m^{4/3}$, improving over the breakthrough $m^{10/7}$ time algorithm of Mądry.

This is based on joint work with Aaron Sidford (https://arxiv.org/abs/1910.14276 and arxiv.org/abs/2003.08929).

computational complexitycomputational geometrycryptography and securitydiscrete mathematicsdata structures and algorithmsgame theorymachine learningquantum computing and informationcombinatoricsinformation theoryoptimization and controlprobability

Audience: researchers in the topic

TCS+

Series comments: Description: Theoretical Computer Science

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