Suppose that a maximum flow has been found in a flow network G = (V, E) using a pusher label algorithm. Give a fast algorithm to find a minimum cut in G.
Answer to relevant QuestionsShow that line 7 of INITIALIZE-PREFLOW can be changed to 7 h[s] ← |V [G]| - 2 without affecting the correctness or asymptotic performance of the generic pusher label algorithm.Prove that the number of comparators in any sorting network is Ω (n lg n).There are two types of professional wrestlers: "good guys" and "bad guys." Between any pair of professional wrestlers, there may or may not be a rivalry. Suppose we have n professional wrestlers and we have a list of r pairs ...Give an O (V + E)-time algorithm to compute the component graph of a directed graph G = (V, E). Make sure that there is at most one edge between two vertices in the component graph your algorithm produces.Suppose that all edge weights in a graph are integers in the range from 1 to |V|. How fast can you make Kruskal’s algorithm run? What if the edge weights are integers in the range from 1 to W for some constant W?
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