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hw2 - tree(right The shortest path tree contains the edges...

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ENGRI 115 Engineering Applications of OR Fall 2007 The Shortest Path Problem I. Homework 2 Due date: Thursday, September 13 in class. References: Lecture notes; Lab 2; Winston 8.1, 8.2. The first two problems are practice problems, DO NOT hand them in. The TAs will be glad to help you if you have any questions. 1. Winston, page 418, Problem 1. Determine a shortest path tree from node 1 to all the other nodes using Dijkstra’s algorithm. 2. Winston, page 418, Problem 2. Determine a shortest path tree from node 1 to all the other nodes using Dijkstra’s algorithm. 3. Winston, page 418, Problem 4. 4. Consider the undirected example from class (see below: the original graph (left) and the shortest path
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Unformatted text preview: tree (right)). The shortest path tree contains the edges that are needed to get via a shortest path to each node (starting from node 1). a. How much must the cost on edge { 1 , 2 } increase in order to force it out of the shortest path tree? How is the shortest path tree going to change? b. How much must the cost on edge { 4 , 6 } decrease so that it becomes part of a shortest path? How will this change alter the shortest path tree? 5. Winston, page 419, Problem 9....
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