Give an efficient algorithm to find the length (number of edges) of a minimum-length negative-weight cycle in a graph.
Answer to relevant QuestionsShow how to express the single-source shortest-paths problem as a product of matrices and a vector. Describe how evaluating this product corresponds to a Bellman-Ford-like algorithm (see Section 24.1).Suppose that we order the edge relaxations in each pass of the Bellman-Ford algorithm as follows. Before the first pass, we assign an arbitrary linear order v1, v2,..., v |v| to the vertices of the input graph G = (V, E). ...Given a flow network G = (V, E), let f1 and f2 be functions from V × V to R. The flow sum f1 + f2 is the function from V × V to R defined by (26.4) (fi + f2) (u, v) = f1 (u, v) + f2(u, v) for all u, v ¬ V. If f1 ...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. How many comparators are there in SORTER [n]?
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