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prelab1

# prelab1 - 11 10 23 22 11 11 1 Find the minimum spanning...

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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 trees. 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. 3 4 1 5 2 5 10 5 40
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Unformatted text preview: 11 10 23 22 11 11 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 the ﬁrst four nodes. Note that this need not be a spanning tree of the graph, since the new node need not be included. Find the optimal solution, and explain why it is optimal....
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