Show that a maximum flow in a network G=(V, E) can always be fo... | Filo

A closer look at network structure: Network edge, applications,... | Filo

In a standard s-t Maximum-Flow Problem, we assume edges have capaci ties, and there is no limit on how much flow is allowed to pass through a node. In this problem, we consider the variant of the Maximum-Flow and Minimum-Cut problems with node capacities. Let G=(V, E) be a directed graph, with source s ∈V, sink t ∈V, and nonnegative node capacities {cv ≥0} for each v ∈V. Given a flow f in this graph, the flow though a node v is defined as f^in (v). We say that a flow is feasible if it satisfies