Abstract
Given a set of n disjoint balls b1, . . ., bn in IRd, we provide a data structure, of near linear size, that can answer (1 \pm ε)-approximate kth-nearest neighbor queries in O(log n + 1/ε^d) time, where k and εare provided at query time. If k and εare provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space; that is, the data structure has sublinear space requirement if k is sufficiently large.
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