 
Summary: SpaceTime Tradeoffs for Approximate Spherical Range Counting
Sunil Arya
Theocharis Malamatos
David M. Mount
Abstract
We present spacetime tradeoffs for approximate spherical
range counting queries. Given a set S of n data points in Rd
along with a positive approximation factor , the goal is to
preprocess the points so that, given any Euclidean ball B,
we can return the number of points of any subset of S that
contains all the points within a (1  )factor contraction of
B, but contains no points that lie outside a (1 + )factor
expansion of B.
In many applications of range searching it is desirable
to offer a tradeoff between space and query time. We
present here the first such tradeoffs for approximate range
counting queries. Given 0 < 1/2 and a parameter
, where 2 1/, we show how to construct a
data structure of space O(nd
log(1/)) that allows us to
