Spatial Skyline Queries on Triangulated Irregular Networks

Abstract

A spatial skyline query is a query to find a set of data points that are not spatially dominated by other data points, given a set of data points P and query points Q in a multidimensional space. The query enumerates the skyline points based on distance in a multidimensional space. However, existing spatial skyline queries can lead to large errors with actual travel distances in geo-spaces because the query is based on the Euclidean distance. We propose a spatial skyline query on triangulated irregular networks (TINs), which are frequently used to represent the surfaces of terrain. We define a new spatial skyline query based on more accurate travel distances considering the TIN distance instead of the Euclidean distance. We also propose an efficient solution method using indexes to find nearest-neighbor points in TIN space and reduce the numbers of unnecessary data points and TIN vertices. The proposed method achieves a computational complexity of O(|P′||Q|N′2 + |P′|2|Q|), where P′ and N′ are the reduced sets of data points and number of TIN vertices, respectively, based on the range of query points. The proposed method can process a query faster than the naive method with Θ(|P||Q|N2 + |P|2|Q|), where N is the number of TIN vertices. Moreover, experiments verify that the proposed method is faster than the naive method by using a spatial index to reduce the numbers of unnecessary data points and TIN vertices.