Cornell, ENGRI 1101
Excerpt: ... ENGRI 115 Engineering Applications of OR Fall 2007 The Minimum Spanning Tree Problem Prelab 1 Name: Objectives: Introduce students to the graph theoretic concept of spanning trees. Show three different combinatorial algorithms for solving the minimum spanning tree problem. Demonstrate a practical use of minimum spanning tree s. Key Ideas: graph subgraph, spanning subgraph, connected subgraph tree greedy algorithm minimality sensitivity analysis Prelab Exercise: Please write your answers on the back of this sheet. Consider the following input for the minimum spanning tree problem. 2 10 11 5 5 11 11 10 22 5 3 23 1 4 40 1. Find the minimum spanning tree in this graph, and give a very simple argument why it is optimal. 2. It turns out that our input was more complicated: only nodes 1 through 4 need to be connected. We may include node 5 if this yields a cheaper solution, but we don't need to. Node 5 is called a Steiner node. We wish to compute the minimum-cost tree that connects ...
Cornell, ENGRI 1101
Excerpt: ... ENGRI 1101: Engineering Applications of OR, Fall 2008 Prelab 3: The Minimum Spanning Tree Problem Name: Netid: Objectives: Introduce students to the graph theoretic concept of spanning trees. 1 Show three dierent combinatorial algorithms for solving the minimum spanning tree problem. Demonstrate a practical use of minimum spanning tree s. Key Ideas: graph, subgraph, spanning subgraph, connected subgraph, tree, greedy algorithm, minimality, sensitivity analysis Reading Assignment: Read Handout 4 on the minimum spanning tree problem. Prelab exercise: Please write your answer on the back of this sheet. Consider the following input for the minimum spanning tree problem. 2 10 11 5 5 11 11 10 22 5 3 23 1 4 40 1. Find the minimum spanning tree in this graph, and give a very simple argument why it is optimal. 2. It turns out that our input was more complicated: only nodes 1 through 4 need to be connected. We may include node 5 if this yields a cheaper solution, but we dont need to. Node 5 is c ...
Cornell, ENGRI 1101
Excerpt: ... 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 457458 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? (c) Considering again the solution on F ...
Pittsburgh, BUSQOM 0050
Excerpt: ... o destination. Example: Ray Design o Must transport beds, chairs, and other furniture items daily from factory to warehouse. o Involves going through several cities (nodes). o Find path with shortest distance in miles. LP Formulation: 3 3. Minimum Spanning Tree (MST) o Minimum-spanning tree problem determines path through network that connects all points. o Most common objective is to minimize total distance of all arcs used in path. o Example: determine best way to connect all of houses to electrical power in a way that minimizes total distance or length of power lines. Example: o Determine least expensive way to provide water and power to each house. o Distance between each house (in hundreds of feet) is shown on network. o Distance between houses 1 and 2 is 300 feet (shown by the 3 on arc connecting houses 1 and 2). o Minimum-spanning tree model to be used to determine minimum total length (of water pipes or power cables) needed to connect all the houses. 4 Procedure for solving MST: ...