Seonglae ChoResearchers Achieve 'Absurdly Fast' Algorithm for Network Flow | Quanta Magazine
Researchers soon started exploring how to apply this advance to the maximum flow problem. The idea is to imagine our highway network as a network of wires and to turn up the resistance on the highways that don't have much available capacity, to discourage electrons from running through them.
https://www.quantamagazine.org/researchers-achieve-absurdly-fast-algorithm-for-network-flow-20220608
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.
https://arxiv.org/abs/2203.00671
