Monochromatic and bichromatic reverse nearest neighbor queries on land surfaces

Finding reverse nearest neighbors (RNNs) is an important operation in spatial databases. The problem of evaluating RNN queries has already received considerable attention due to its importance in many real-world applications, such as resource allocation and disaster response. While RNN query processing has been extensively studied in Euclidean space, no work ever studies this problem on land surfaces. However, practical applications of RNN queries involve terrain surfaces that constrain object movements, which rendering the existing algorithms inapplicable. In this paper, we investigate the evaluation of two types of RNN queries on land surfaces: monochromatic RNN (MRNN) queries and bichromatic RNN (BRNN) queries. On a land surface, the distance between two points is calculated as the length of the shortest path along the surface. However, the computational cost of the state-of-the-art shortest path algorithm on a land surface is quadratic to the size of the surface model, which is usually quite huge. As a result, surface RNN query processing is a challenging problem. Leveraging some newly-discovered properties of Voronoi cell approximation structures, we make use of standard index structures such as an R-tree to design efficient algorithms that accelerate the evaluation of MRNN and BRNN queries on land surfaces. Our proposed algorithms are able to localize query evaluation by accessing just a small fraction of the surface data near the query point, which helps avoid shortest path evaluation on a large surface. Extensive experiments are conducted on large real-world datasets to demonstrate the efficiency of our algorithms.