An Approximate Distribution for the Random Distance between Sets of Rectangles

Abstract

A moment-based methodology is proposed for approx- imating the distribution of the distance between two random points belonging to sets that are composed of rectangles. The resulting density approximants are expressed in terms of polynomially adjusted beta density functions. Two norms are being considered: the L1 norm referred to as the Manhattan distance and the L2 norm which corresponds to the Euclidean distance. A few illustrative examples will be presented and certain applications to transportation and routing problems will be pointed out.