Range searching in low-density environments

Abstract

We define a set of arbitrarily-shaped objects in R(d) to be a low-density environment if any axis-parallel hypercube intersects only few objects of comparable or larger size. Generalizing and simplifying previous results for fat objects, we present a data structure for point location in a low-density environment, and we show how this data structure can be extended to perform range search queries with query ranges of size comparable to the smallest object.