A General Technique for Top-k Geometric Intersection Query Problems

Abstract— A General Technique for Top-k Geometric Intersection Query Problems. In a top-k Geometric Intersection Query (top-k GIQ) problem, a set of n weighted, geometric objects in Rd is to be preprocessed into a compact data structure so that for any query geometric object, q, and integer k > 0, the k largest-weight objects intersected by q can be reported efficiently. While the top-k problem has been studied extensively for non-geometric problems (e.g., recommender systems), the geometric version has received little attention. This paper gives a general technique to solve any top-k GIQ problem efficiently. The technique relies only on the availability of an efficient solution for the underlying (non-top-k) GIQ problem, which is often the case. Using this, asymptotically efficient solutions are derived for several top-k GIQ problems, including top-k orthogonal and circular range search, < Final Year Projects > point enclosure search, halfspace range search, etc. Implementations of some of these solutions, using practical data structures, show that they are quite efficient in practice. This paper also does a formal investigation of the hardness of the top-k GIQ problem, which reveals interesting connections between the top-k GIQ problem and the underlying (non-top-k) GIQ problem.