solution to flow network problem

(Latest Revision: Dec 1, 2022)

Solution to the 2023 Flow Network Problem

For this problem, the A-side of the minimum cut is {s, b, c, d}. No other nodes are reachable from the source, s, in the final version of the residual graph, G_f. The value of the max flow, v(f*), is the sum of the flows on the edges leaving the source node s in G. That sum is v(f*) = 2 + 5 + 7 = 14. The capacity of the min cut is the sum of the capacities of the edges (in G) leaving the A-side of the cut, 2 + 1 + 5 + 6 = 14 = v(f*). These calculations verify that the max value of an s-t flow is equal to the min capacity of an s-t cut, which, according to the "Max-Flow, Min-Cut Theorem," is true for any flow network.