Question: Q)a)(T/F) Let G = (V, E) be a directed graph with arbitrary (possibly negative) edge weights. Suppose, s,t ? V are two distinct vertices in

Q)a)(T/F) Let G = (V, E) be a directed graph with arbitrary (possibly negative) edge weights. Suppose, s,t ? V are two distinct vertices in G such that all directed paths from s to t in G contain no cycles, and at least one such path exists. Then, the Bellman-Ford algorithm, starting from a source vertex s, will correctly calculate the weight of a shortest path from s to t, even if G contains negative cycles.

b) (T/F) Let G = (V, E) be a directed graph with arbitrary (possible negative) edge weights, but no negative cycles. Let k be a positive integer. Suppose that, for all pairs of vertices u, v ? V, the graph G contains some directed path from u to v that uses ? k edges. Then, the Bellman-Ford algorithm correctly outputs shortest paths when modified to only perform k rounds of relaxations, instead of the usual |V|-1 rounds.

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