Modify dijkstra''s algorithm

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Reference no: EM13968291

1. Suppose all the edge weights in a graph are integers between 1 and |E|. How fast can Dijkstra's algorithm be implemented?

2. Write a program to solve the single-source shortest-path problem.

3. a. Explain how to modify Dijkstra's algorithm to produce a count of the number of different minimum paths from to w.

b. Explain how to modify Dijkstra's algorithm so that if there is more than one minimum path from to w, a path with the fewest number of edges is   chosen.

4. Find the maximum ?ow in the network.

5. Suppose that = (VE) is a tree, is the root, and we add a vertex and edges of in?nite capacity from all leaves in to t. Give a linear-time algorithm to ?nd a maximum ?ow from to t.

Reference no: EM13968291

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