A Voronoi-Based Group Reverse k Farthest Neighbor Query Method in the Obstacle Space

Abstract

With the rapid development of intelligent transportation and geographic information system, spatial data query technology has attracted the attention of many scholars. Among them, the reverse farthest neighbor query from the data point to find the target point as its farthest adjacent data points, used to obtain target set of weak influence. Its research results have been widely applied to facility location, earthquake relief, marketing and other major areas. Thus, the research of reverse furthest neighbor query technology is of great significance. However, the existing methods only deal with a single query point, and do not consider how to obtain the optimal farthest neighbor position of group reverse when the number of query points changes from one to a group. In addition, considering it is difficult to avoid some geographical location restrictions in the real situation, the existing studies are limited to road network or Euclidean space simplely, without taking the existence of obstacles into consideration. To this end, this paper proposed the V-OGRkFN(Voronoi-Obstacle Group Reverse $k$ Farthest Neighbor) algorithm. Firstly, the algorithm gets the minimum cover circle of query points which are considered into a whole. Secondly, we use the framework based on the filtering and refining process of query by pruning strategy based on Voronoi diagram's properties. Then we get the candidate set using the theorem of transformation between $k$ nearest neighbors and $k$ farthest neighbors. Finally, the refining algorithm is given to get the final results. V-OGRkFN algorithm shows great performance of reverse $k$ farthest neighbor query through the specific comparative experimental analysis.