Lecture 9 & 10 : Local Search Algorithm for k - median Problem ( contd . ) , k - means Problem
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چکیده
Let us define some notation which will help us analyze the algorithm. L := A solution (k-subset) returned by Local Search. Copt := An optimal solution for the k-median problem. We will eventually show that Cost(L) ≤ 5 · Cost(Copt). For any p ∈ P,C ⊆ P, NN(p, C) := c̄ ∈ C that minimizes d(p, ·). So d(p,NN(p, C)) = d(p, C) by definition. Also, for any C ⊆ P, c̄ ∈ C, Cluster(C, c̄) := {q ∈ P | NN(q, C) = c̄}. For an optimal center ō ∈ Copt,
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