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Mathematics

Network Flow Problems and the Max-Flow Min-Cut Theorem

Quick fact

The max-flow min-cut theorem was proven independently by Ford and Fulkerson in 1956 and by Elias, Feinstein, and Shannon in the same year, and it led to a fundamental algorithm that runs in polynomial time for many networks.

Why this is interesting

Imagine water flowing through a network of pipes, each with a limited capacity. You'd think the answer depends on every pipe, but a surprising theorem tells you that the bottleneck is actually one single cut of the pipes. What is that cut?