Prove that the generic pusher label algorithm spends a total of only O(V E) time in performing all the O(V2) relabel operations.
Answer to relevant QuestionsSuppose 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. Prove that any sorting network on n inputs has depth at least lg n.Give an example of a directed graph G = (V, E), a source vertex s ¬ V, and a set of tree edges E π ¬ E such that for each vertex v ¬ V, the unique path in the graph (V, E π) from s to v is a shortest path in G, ...Another way to perform topological sorting on a directed acyclic graph G = (V, E) is to repeatedly find a vertex of in-degree 0, output it, and remove it and all of its outgoing edges from the graph. Explain how to implement ...Given a graph G and a minimum spanning tree T, suppose that we decrease the weight of one of the edges in T. Show that T is still a minimum spanning tree for G. More formally, let T be a minimum spanning tree for G with edge ...
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