Question

Problem 9 Consider the directed network on vertices V s, 1,2,3, 4,5,t) given by the following list. An element of this list has the forn (í,j,c) where (i,j) is an are of the network, and c is the capacity of are (i.j) (3, 4,2), (3,,15), (3, 5,11), (3, t, 12, (4,5,9), (4, t, 15), (5,t,7) ·What is the maximuln 8 → t flow in this network? (You may use AMPL to compute this.) What is a minimum cut? EXTRA CREDIT; mandatory for PhD students: Recall the def nition of the cut value C(S) for subsets S CV, s E S, t gS. Prove that C is a submodular function, that is for SIS V, s E S,, t i, i = 1, we have

Answer 1

กา 15 at 15cm -808 k lo! 历ナ.lro