Slides4_5

# Slides4_5 - Lecture 4/5 Shortest Path Problems Example...

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1 Lecture 4/5 Shortest Path Problems Example Following your suggestions (based on MST), the executive board of your company built the connecting wires between the cities. However, they chose to include additional power lines (to have a reliable network). Now they approach you again hoping to get an answer for a somewhat different problem: A power plant has been built in Albany, and the produced power should be sent to Trenton. But there are different ways to achieve this in the constructed network. The specific question is: What is the shortest path in the network from Albany to Trenton?

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2 Example 1 1 2 3 4 5 6 3 3 2 3 4 2 2 Albany Trenton (see Winston, Example 1, page 414) Given a graph with edge weights c ij 0. Find a shortest path from node 1 to node 6. Solution: Dijkstra’s algorithm Idea: Instead of computing the shortest path from node 1 to 6, we compute all shortest paths from node 1 to node i (i=2,..,6).