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November 22 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 22, 2005
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November 22, 2005 Agenda Last week The Class P The Class NP Today More on the class NP
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November 22, 2005 Solving vs. verifying What if we can’t  solve  the problem in O(n k ) time? Given a problem and a potential solution, can we  verify  the solution is correct?
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November 22, 2005 Example The vertex cover problem Given a graph G = <V,E> and a number k in N, does  there exist a subset V’ of V such that |V’| = k For every (u,v) E, either u V’ or v V’
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November 22, 2005 Vertex cover
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November 22, 2005 The vertex cover problem There is no known polynomial solution to the  vertex cover problem What if we have a potential solution Can we verify it in O(n k ) time?
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November 22, 2005 Verifier M accepts <V,E,k,V’> if and only if |V’| = k and 
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