Lecture 05 : K - wise Independence and - Bias
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چکیده
Given a graph G on a vertex set V , MaxCut is the problem of finding a partition of V so that the number of edges cut is as large as possible. MaxCut has a simple random approximation algorithm. Given a graph G = (V,E), output a random partition (R,B) of V . Specifically, for each vertex v ∈ V , put v in R or B with probability 1 2 . Theorem 3. The expected number of edges cut by this algorithm is at least 12 |E|, that is E[number of edges cut] ≥ 1 2 |E|. Proof. For an edge e ∈ E, define the random variable
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