On the expected weight of the theta graph on uncertain points

Given a point set S Rd, the -graph of S is as follows: for each point s 2 S, draw cones with apex at s and angle and connect s to the point in each cone such that the projection of the point on the bisector of the cone is the closest to s. One can dene the - graph on an uncertain point set, i.e. a point set where each point si exists with an independent probability i 2 (0; 1]. In this paper, we propose an algorithm that computes the expected weight of the -graph on a given uncertain point set. The proposed algorithm takes O(n2(n2; n)2d) time and O(n2) space, where n is the number of points, d and are constants, and is the inverse of the Ackermann's function.