Group Location Selection Queries over Uncertain Objects

Given a set of spatial objects, facilities can influence the objects located within their influence regions that are represented by circular disks with the same radius r. Our task is to select the minimum number of locations such that establishing a temporary facility at each selected location would ensure that all the objects are influenced. Aiming to solve this location selection problem, we propose a novel kind of location selection query, called group location selection (GLS) queries. In many real-world applications, every object is usually located within an uncertainty region instead of at an exact point. Due to the uncertainty of the data, GLS processing needs to ensure that the probability of each uncertain object being influenced by one facility is not less than a given threshold τ. An analysis of the time cost reveals that it is infeasible to exactly answer GLS queries over uncertain objects in polynomial time. Hence, this paper proposes an approximate query framework for answering queries efficiently while guaranteeing that the results of GLS queries are correct with a bounded probability. The performance of the proposed methods of the framework is demonstrated by theoretical analysis and extensive experiments with both real and synthetic data sets.