HW5 - CSE 830 Design and Theory of Algorithms Homework#5...

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CSE 830: Design and Theory of Algorithms Homework #5 Due Monday, April 21 st 2008, 3pm Each problem should be solved on a separate sheet of paper to facilitate grading. Limit the solution of each problem to one sheet of paper. Please don't wait until the last minute to look at the problems. 1. The Graph-isomorphism problem is an open problem; no one has yet been able to prove it to be a hard problem, yet no polynomial time algorithm has been constructed either. Show that Graph Isomorphism is in NP by describing what certificate should be returned with a “yes” answer, and how that certificate can be verified in polynomial time. Analyze the time complexity for this verification. 2. The Subgraph-isomorphism problem is much easier to deal with than its full-graph counterpart. This problem takes two graphs G 1 and G 2 and asks whether G 1 can be found as a subgraph in G 2 . Show that the subgraph-isomorphism problem is NP-complete. 3. Implement an algorithm to solve the vertex cover problem. To do this, use the Minimum Dominating Set program implemented by one of your group members. Write only two
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