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Unformatted text preview: ENGRI 115 Engineering Applications of OR Fall 2007 The Minimum Spanning Tree Problem Lab 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 trees. Key Ideas: • graph • subgraph, spanning subgraph, connected subgraph • tree • greedy algorithm • minimality • sensitivity analysis 1 Part #1 - Minimum Spanning Tree Application: Communication Network Design You are the engineer in charge of designing a new high speed fiber optic Internet network between the major centers of central Europe. Your objective is to design a system that connects all the major cities of central Europe at a minimum cost. However, so that this network can be brought online quickly, we must install the fiber optic line within existing physical infrastructure. The possible physical cable routes between cities and the cost of installing the fiber optic cable (in millions of dollars) are given by the data shown on the map. How do you suppose you would go about designing such a system? Since you can only use the edges shown in the attached graph, you must choose a subgraph of the given graph, or in other words, a subset of the possible edges. Every location must be serviced which means that the subgraph must be spanning. You should be able to get to any location from any other location. This means the subgraph should be connected. Because you are trying to minimize cost, the subgraph should also be minimal, meaning that you cannot remove any of the edges while maintaining the other necessary properties. A minimal connected spanning subgraph is called a spanning tree (it thus contains no cycles). There are many other ways of defining trees. In operations research terminology, we want to find a minimum spanning tree of the given graph....
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- Spring '05
- Kruskal's algorithm, Prim, Kruskal