Coresets for Discrete Integration and Clustering
نویسنده
چکیده
Given a set P of n points on the real line and a (potentially in nite) family of functions, we investigate the problem of nding a small (weighted) subset S ⊆ P , such that for any f ∈ F, we have that f(P ) is a (1 ± ε)-approximation to f(S). Here, f(Q) = ∑ q∈Q w(q)f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study this problem, and provide tight bounds on the size S for several families of functions. As an application, we present some coreset constructions for clustering.
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