Hypersphere dominance: an optimal approach

Hyperspheres are commonly used for representing uncertain objects (in uncertain databases) and for indexing spatial objects (in spatial databases). An interesting operator on hyperspheres called dominance is to decide for two given hyperspheres whether one dominates (or is closer than) the other wrt a given query hypersphere. In this paper, we propose an approach called Hyperbola which is optimal in the sense that it gives neither false positives nor false negatives and runs in linear time wrt the dimensionality. To the best of our knowledge, Hyperbola is the first optimal approach for the dominance problem on hyperespheres with any dimensionality. We also study an application of the dominance problem which relies on the dominance operator as the core component. We conducted extensive experiments on both real and synthetic datasets which verified our approaches.