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Unformatted text preview: CS 435 : Linear Optimization Fall 2008 Lecture 17: Graph Algorithms: Matchings Lecturer: Sundar Vishwanathan Computer Science & Engineering Indian Institute of Technology, Bombay In this lecture we reviewed old material. Mostly data structures. We noted that graphs will be repre- sented by adjacency lists for this course. We then de ned a matching, given below. 1 Matching Definition 1 A matching in a graph is a set of edges, no two of which share an end-point. Our interest is the following problem: Input: Graph G . Output: Find a maximum cardinality matching in G . We wish to design an algorithm (polynomial time) for this problem. How do we begin our design? The only real design technique is induction, which you should try out rst. We will pass this for the time being. One way is to start with some matching and then see if you can improve this. For the greedy method, you would have tried some kind of local exchanges. They do not quite work here....
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