(Approximate) Conic Nearest Neighbors and the induced Voronoi Diagram

For a given point set in Euclidean space we consider the problem of finding (approximate) nearest neighbors of a query point but restricting only to points that lie within a fixed cone with apex at the query point. We investigate the structure of the Voronoi diagram induced by this notion of proximity and present approximate and exact data structures for answering cone-restricted nearest neighbor queries. In particular we develop an approximate Voronoi diagram of size O((n/d)log(1/)) that can be used to answer cone-restricted nearest neighbor queries in O(log(n/)) time.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Stefan Funke, Theocharis Malamatos, Domagoj Matijevic, Nicola Wolpert
• Keywords: CCCG 2006, CCCG 2007, Cone-restricted Nearest Neighbor, Nearest Neighbor, Nearest Neighbor Queries