prelab7 - weighted matching relies on something called the...

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ENGRI 115 Engineering Applications of OR Fall 2007 The Assignment Problem Prelab 7 Name: Objectives: Show how to find maximum weight matching in bipartite graphs using the Hungarian Algorithm. Key Ideas: weighted matching, maximum weighted matching maximum weighted matching in bipartite graphs = assignment problem weighted node cover, node weights exposed node with respect to a matching, alternating tree rooted at an exposed node outer nodes, inner nodes in an alternating tree Prelab Exercise: Please write your answer on the back of this sheet (or an attached paper). Cardinality matching is a special case of weighted matching where the edges in the graph have weights 1 and the edges not in the graph have weights 0. (Convince yourself that this is true.) We have already seen how to find a minimum node cover for a bipartite graph. The Hungarian Algorithm for finding a maximum
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Unformatted text preview: weighted matching relies on something called the weighted node cover which is a generalization of the node cover for the cardinality case. The goal of this prelab exercise is to draw a parallel between the cardinality and the weighted case. A-3, B-1, C-4 and E-2 is a maximum (cardinality) matching for the graph below (matching edges are bold). a. Draw an alternating tree to show that the indicated matching is maximum. b. Find a minimum node cover (circle the nodes in the minimum node cover in the original graph). What is the size of the minimum node cover? c. Is there an exposed node (wrt the matching) which is in the minimum node cover? Why? Is there a matching edge with both endpoints in the minimum node cover? Why? A B C D E 1 2 3 4 5...
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This note was uploaded on 06/01/2008 for the course ENGRI 1101 taught by Professor Trotter during the Fall '05 term at Cornell University (Engineering School).

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prelab7 - weighted matching relies on something called the...

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