175 Years of linear programming: max flow = min cut

Abstract

The theory of flows in networks began to evolve in the early 1950's.The various linear optimisation questions that could be asked of flows in conserving networks turned out to be neat combinatorial specialisations of linear programming. The simplex method (and its variants) turned out to have very pretty combinatorial interpretations on networks. The algebraic dexterity of linear programming duality led to a unified treatment of many deep theorems in graph theory and combinatorics. In this part, the last of the series on linear programming, we will see glimpses of the theory of network flows through a specific flow optimisation problem - the maximum flow problem.