Proximity Queries on Terrain Surface

Due to the advance of the geo-spatial positioning and the computer graphics technology, digital terrain data has become increasingly popular nowadays. Query processing on terrain data has attracted considerable attention from both the academic and the industry communities. Proximity queries such as the shortest path/distance query, k nearest/farthest neighbor query, and top-k closest/farthest pairs query are fundamental and important queries in the context of the terrain surfaces, and they have a lot of applications in Geographical Information System, 3D object feature vector construction, and 3D object data mining. In this article, we first study the most fundamental type of query, namely, shortest distance and path query, which is to find the shortest distance and path between two points of interest on the surface of the terrain. As observed by existing studies, computing the exact shortest distance/path is very expensive. Some existing studies proposed ϵ-approximate distance and path oracles, where ϵ is a non-negative real-valued error parameter. However, the best-known algorithm has a large oracle construction time, a large oracle size, and a large query time. Motivated by this, we propose a novel ϵ-approximate distance and path oracle called the Space Efficient distance and path oracle (SE), which has a small oracle construction time, a small oracle size, and a small distance and path query time, thanks to its compactness of storing concise information about pairwise distances between any two points-of-interest. Then, we propose several algorithms for the k nearest/farthest neighbor and top-k closest/farthest pairs queries with the assistance of our distance and path oracle SE. Our experimental results show that the oracle construction time, the oracle size, and the distance and path query time of SE are up to two, three, and five orders of magnitude faster than the best-known algorithm, respectively. Besides, our algorithms for other proximity queries including k nearest/farthest neighbor queries and top-k closest/farthest pairs queries significantly outperform the state-of-the-art algorithms by up to two orders of magnitude.