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Determine also the minimum cut 1 u 2 4 u d d 0

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Unformatted text preview: minimum cut. 1 u [2, 4] u d d  [0, 4] d T d d  [1, 3] d w v E u d d  [1, 3] d [0, 3] T d d  d du [−1, 1] dus d d [1, 3] d d   d d [0, 4] d [1, 2] d [1, 5]  d  d d d du E du u r [1, 3] [−1, 1] x y 4. Given the digraph below with source r and sink s. The two values between brackets given at each arc give the demand and the capacity of that arc. Search for a feasible ﬂow by use of the method presented in the course. Give a feasible ﬂow if there is one, otherwise explain why there is no feasible ﬂow. u u d d  [2, 5] d [1, 2] v u d d  [0, 1] d [0, 2] E T T d d d  d  [1, 2] d w d du dus u r [2, 4] [1, 3] d d [0, 3] d d   d d [1, 3] d [2, 4] d [0, 1]  d  d d d E du du x [0, 2] y 5. Consider the network (V, A) below with weights on the nodes. The problem is to ﬁnd a closure (a closure is a subset C of V such that no arc (i, j ) ∈ A has i ∈ C and j outside C ) with maximum total weight. Translate this problem into a max-ﬂow min-cut problem and solve it. 2u T 1u 3u E c −2 u ' −1 u c E −1 u 2 c E −1 u...
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