Let P be a set of n points in d-dimensional Euclidean space, where each of the points has integer coordinates from the range [−∆, ∆], for some ∆ > 1. Let ε > 0 be a given parameter. We show that there is subset Q of P , whose size is polynomial in (log ∆/ε), such that for any k slabs that cover Q, their ε-expansion covers P. In this result, k and d are assumed to be constants. The set Q can also be computed efficiently, in time that is roughly n times the bound on the size of Q. Besides… CONTINUE READING