Approximate Range Queries for Clustering

03/11/2018

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by   Eunjin Oh, et al.

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We study the approximate range searching for three variants of the clustering problem with a set P of n points in d-dimensional Euclidean space and axis-parallel rectangular range queries: the k-median, k-means, and k-center range-clustering query problems. We present data structures and query algorithms that compute (1+ε)-approximations to the optimal clusterings of P∩ Q efficiently for a query consisting of an orthogonal range Q, an integer k, and a value ε>0.