Assume that a set of imprecise points is given, where each point is specified by a region in
which the point may lie. We study the problem of computing the smallest and largest …

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of
points, is an important and widely studied problem in many fields, and it has a wide range of …

We consider problems on data sets where each data point has uncertainty described by an
individual probability distribution. We develop several frameworks and algorithms for …

An assumption of nearly all algorithms in computational geometry is that the input points are
given precisely, so it is interesting to ask what is the value of imprecise information about …

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle
data uncertainty inherent in many applications, including sensor databases, location-based …

Voronoi diagrams appear in many areas in science and technology and have numerous
applications. They have been the subject of extensive investigation during the last decades …

We study the complexity of geometric minimum spanning trees under a stochastic model of
input: Suppose we are given a master set of points s1, s_2,..., sn in d-dimensional Euclidean …

Motivated by real-life situations in which exact input data is not available initially but can be
obtained at a cost, one can consider the model of computing with uncertainty where the …

Suppose we want to compute the Delaunay triangulation of a set P whose points are
restricted to a collection ℛ of input regions known in advance. Building on recent work by …

High-density airborne light detection and ranging (LiDAR) data with point densities over 50
points/provide new opportunities, because previously inaccessible quantities of an …