Abstract: To overcome the limitation of query objects in group reverse k nearest neighbor (GRkNN) query, this paper proposes the group reverse k nearest neighbor query method based on Voronoi diagram (V_GRkNN). The proposed method finds data points that take any point in the query objects set as one of their k nearest neighbors. In the practical application, V_GRkNN query can be used to evaluate the influence of a group of query objects. Firstly, the query points set Q is optimized in order to reduce the effect of the query points number on query efficiency, the data points set P is pruned to reduce the searching ranges. And then according to the pruning strategies based on Voronoi diagram, the candidate set is filtered. Finally, a refinement process is used to get the query's final results. The V_GRkNN method greatly improves the query speed and efficiency. Theoretical research and experiments show that the efficiency of the proposed V_GRkNN method obviously outperforms other algorithms.

Key words: Voronoi diagram, reverse k nearest neighbor, group reverse k nearest neighbor, index structure

摘要： 为了改进现有的组反k最近邻查询算法的查询速度与准确度，提出了一种基于Voronoi图的组反k最近邻查询方法（group reverse k nearest neighbor guery method based on Voronoi diagram，V_GRkNN）。该方法获得的结果集是将这组查询点中任意一点作为kNN的数据点集合，在实际应用中可以用来评估一组查询对象的影响力。该方法的特点是首先对查询点集Q进行优化处理，降低查询点数量对查询效率的负面影响；接着对数据点集P进行约减，缩小查询搜索范围；然后根据基于Voronoi图的剪枝策略对候选集进行过滤；最后经过精炼获得GRkNN查询的结果集。该方法在数据集处理阶段很大程度上提高了查询速度，在过滤、精炼阶段利用Voronoi图的特性提高了查询的准确性。理论研究和实验表明，所提方法的效率明显优于可选的已有方法。

关键词: Voronoi图, 反k最近邻, 组反k最近邻, 索引结构