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 . 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.

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A visible k nearest neighbor (VkNN) query retrieves k objects that are visible and nearest to the query object, where "visible" means that there is no obstacle between an object and the query object. Existing studies on the VkNN query have focused on static data objects. In this paper we investigate how to process the query on moving objects continuously. We propose an effective filtering-andrefinement framework for evaluating this type of queries. We exploit spatial proximity and visibility properties between the query object and data objects to prune search space under this framework. A detailed cost analysis and a comprehensive experimental study are conducted on the proposed framework. The results validate the effectiveness of the pruning techniques and verify the efficiency of the proposed framework. The proposed framework outperforms a straightforward solution by an order of magnitude in terms of both communication and computation costs.

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