Localized geometric query problems

Localized geometric query problems

A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects P in the plane, so that for any arbitrary query point q, the largest circle that contains q but does not contain any member of P , can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.

On Geometric Path Query Problems

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 pre-processed 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 sy...

Complete Geometric Query Languages

We extend Chandra and Harel s seminal work on computable queries for re lational databases to a setting in which also spatial data may be present using a constraint based data model Concretely we introduce both coordinate based and point based query languages that are complete in the sense that they can express precisely all computable queries that are generic with respect to certain classes of...

Extremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric

A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...