We study the expected number of interior vertices of degree i in a triangulation of a point set S, drawn uniformly at random from the set of all triangulations of S, and derive va...
We present simple, fully dynamic and kinetic data structures, which are variants of a dynamic two-dimensional range tree, for maintaining the closest pair and all nearest neighbors...
Range searching is a well known problem in the area of geometric data structures. We consider this problem in the context of approximation, where an approximation parameter ε >...
Active structures capable of responding to external stimulii represent the emerging frontier in structural design. Robust and real-time sensing, control, and actuation pose fundame...
In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets, called a quadtreap. This data structure is a randomized, balanced ...