Nearest and farthest spatial skyline queries under multiplicative weighted Euclidean distances

Abstract

Consider two point sets in the plane, a set of points of interest and a set of query points that is used to establish distance restrictions with respect to the set of points of interest. A nearest/farthest spatial skyline query retrieves the subset of desirable or relevant points of interest, called skyline points, such that no other point of interest is simultaneously closer to/farther from all the query points. The nearest/farthest top- spatial skylines, are the best nearest/farthest spatial skylines among the existent ones. All these queries find applications in decision-making support systems, facility location, crisis management and in trips or events planning. To take into account that each point of interest has a different importance, a weight is assigned to each of them and multiplicative weighted Euclidean distances are used. In this paper, we study, for the first time, the nearest and farthest spatial skyline queries when multiplicative weighted Euclidean distances are considered. We prove that most of the properties of the traditional non weighted nearest and farthest spatial skyline queries are no longer true under the weighted Euclidean distance and, consequently, the strategies used for solving non weighted spatial skyline queries are not usable in the weighted case. We present a sequential and a parallel algorithm, to be run on the CPU and on a Graphics Processing Unit, respectively, for solving nearest/farthest weighted spatial skyline queries and to extract the nearest/farthest top- spatial skylines. We provide the time and space complexity analysis of both algorithms together with their theoretical comparison. We also have developed a simple interface to deal with weighted spatial skyline queries which allows to visualize and store in a file the obtained spatial skylines. Finally, we present and discuss experimental results obtained with the implementation of the proposed sequential and parallel algorithms