Intersections with random geometric objects

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target objects which may or may not be random: a line segment, a Voronoi diagram, a minimum spanning tree, a Gabriel graph, a relative neighborhood graph, a Hamiltonian circuit, a furthest point Voronoi diagram, a convex hull, a k-dimensional tree, and a rectangular grid. ¢ 1998 Elsevier Science B.V.