Question: Network flows problem. Could you explain the answer in detail, please? Max-Flow with Node Capacities In a standard Max-Flow problem, we assume that edges have

Network flows problem. Could you explain the answer in detail, please?

Network flows problem. Could you explain the answer in detail, please? Max-Flow

Max-Flow with Node Capacities In a standard Max-Flow problem, we assume that edges have capacities, and there is no explicit limit on how much flow is allowed to pass through a node. We now consider a variant of the standard problem where nodes, not edges, have capacities. Let G= (V, E) be a directed graph, with source s E V, sink t EV, and nonnegative node capacities cy for each v EV. Given a flow f in this graph, the flow through a node v is defined as fin(v). We call a flow feasible if it satisfies the usual flow- conservation constraints and the node-capacity constraints: fin(v)

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