lab2 - ENGRI 115 Engineering Applications of OR Fall 2007...

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ENGRI 115 Engineering Applications of OR Fall 2007 The Shortest Path Problem Lab 2 Name: Objectives: Introduce students to the concept of a shortest path tree Show students the inner workings of a combinatorial algorithm Demonstrate the usefulness of sensitivity analysis in problem solving Show students that we use crude optimization algorithms in our everyday lives Demonstrate the concept of the triangle inequality Key Ideas: shortest path Dijkstra’s Algorithm shortest path tree triangle inequality sensitivity analysis combinatorial optimization Prelab Exercise: Please write your answer on the back of this sheet. You are the person sitting in the traffic booth right across from the entrance to the Engineering Library. Motorists arrive frequently and ask you for the shortest path between certain points on campus. Even though you have a good map in front of you, it takes quite a while to compute the shortest path requests since the campus is large with many points of interest. You would like to prepare for these requests in advance. You find a big ball of string, a precise ruler, and a pair of scissors along with the book “Teach Yourself the Art of Knots” in the booth, and you suspect these might help to solve your problem. How? You can assume that all roads on campus are two-way. (Hint: Think about first building a “string model” of the road system on campus ...) Would the same approach work if some of the roads were one-way? 1
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Part #1 - Dijkstra’s Algorithm You are a pizza delivery person for Good Pizza, Inc. Good Pizza is located on Cornell’s campus and guarantees delivery in 30 minutes or less anywhere in Tompkins County. In order to maximize the amount of your tips, you want to deliver as many pizzas as you can and deliver them as fast as you can. Therefore, you would like to know the quickest way of getting from the pizza shop to various parts of Tompkins County. Because of speed limits and various geographical obstacles (of which there are many in Tompkins County), it is not always best to take the route that covers the shortest distance. For instance, to get to Groton from the
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