CS 294 : PCP and Hardness of Approximation February
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چکیده
1. Max-Cut – problem definiton: Given an undirected graph G = (V,E), find a partition of the vertex set V = S ∪ S̄ that maximizes the number of cut-edges (edges with an endpoint in S and an endpoint in S̄). Examples: A clique, a bipartite graph, an odd cycle. The problem is NP-hard [7]. Can be approximated within factor 1/2 [11]. Exercise 1: Show that local search (iteratively move to the other side a vertex if more than half of its neighbors are in the same side, while possible) yields 1/2-approximation. Exercise 2: Show that by randomly assigning vertices to either S or S̄ the expected number of cut-edges is at least |E|/2.
منابع مشابه
CS 286 . 2 Lecture 1 : The PCP theorem , hardness of approximation , and multiplayer games Scribe :
Our first formulation gives the theorem its name (PCP = Probabilistically Checkable Proof). It states that, provided that one is willing to settle for a probabilistic decision process that errs with small probability, all languages in NP have proofs that can be verified very efficiently: only a constant number of symbols of the proof need to be evaluated! To state this formally we first need th...
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