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Lec20PolyR2 - vertices-A vertex cover is a set of vertices...

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Paul Bates Class Notes 4-18-05 3 SAT reduced to Vertex-Cover - Assuming there’s a polynomial solution to Vertex-cover, we will solve 3-SAT in polynomial time. Given an input w to 3-SAT, we will construct a function (in polynomial time), f such that f(w) is an element of Vertex-Cover iff w is an element of 3-SAT. Vertex-Cover - Given a graph G and an integer k, does there exist a vertex cover of G using k
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Unformatted text preview: vertices?-A vertex cover is a set of vertices such that for each edge in G, at least 1 vertex in the set is incident upon it. x 1 , x 2 , … x n # clauses = l # variables = m For each clause, build a triangle: x1 = T x2 = F All triangles and bars are covered. Now show that the extra edges are covered:...
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