# Question: Express the single pair shortest path problem as a linear

Express the single-pair shortest-path problem as a linear program.

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Show how a system of difference constraints can be solved by a Bellman-Ford-like algorithm that runs on a constraint graph without the extra vertex v0. Show 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).Let G = (V, E) be a weighted, directed graph that contains no negative-weight cycles. Let s ¬ V be the source vertex, and let G be initialized by INITIALIZE-SINGLE-SOURCE (G, s). Prove that there exists a sequence of |V | - ...Prove that for any pair of vertices u and v and any capacity and flow functions c and f, we have cf (u, v) + cf (v, u) = c(u, v) + c(v, u).Let G = (V, E) be a flow network with source s, sink t, and an integer capacity c (u, v) on each edge (u, v) ¬ E. Let C = max (u, v) Ec (u, v). a. Argue that a minimum cut of G has capacity at most C ...Post your question