HW1_mst - ENGRI 115 Engineering Applications of OR Fall...

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Unformatted text preview: ENGRI 115 Engineering Applications of OR Fall 2007 The Minimum Spanning Tree Problem Homework 1 Due date: Thursday, September 6, 2007 ; by 10.10am at the beginning of the lecture. Place your homework in the box that I will provide in the class room. References: Lecture notes, Recitation 1, Winston chapter 8.6. The first two problems are practice problems. DO NOT hand them in. Your TAs will be glad to help you if you have any questions. 1. Winston, page 459, Problem 1. 2. Winston, page 459, Problem 2. 3. For this problem we will consider Example 8, page 457–458 in the Winston book (same example as in the lecture). (a) Is the optimum solution to this problem unique? If yes, explain why, if not, give a different optimum solution. (b) Considering the optimum spanning tree given on page 458 (Figure 49d), how much must the cost on edge { 4 , 5 } increase in order to force it out of the optimum spanning tree? Which edge will enter to replace { 4 , 5 } when this happens?...
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