APPROXIMATE QUERY AND CALCULATION OF RNN_k BASED ON VORONOI CELL

Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data points which use a query point as one of their k nearest neighbors. To answer the RNNk of queries efficiently, the properties of the Voronoi cell and the space-dividing regions are applied. The RNNk of the given point can be found without computing its nearest neighbors every time by using the rank Voronoi cell. With the elementary RNNk query result, the candidate data points of reverse nearest neighbors can he further limited by the approximation with sweepline and the partial extension of query region Q. The approximate minimum average distance （AMAD） can be calculated by the approximate RNNk without the restriction of k. Experimental results indicate the efficiency and the effectiveness of the algorithm and the approximate method in three varied data distribution spaces. The approximate query and the calculation method with the high precision and the accurate recall are obtained by filtrating data and pruning the search space.

An evaluation and query algorithm for the influence of spatial location based on RkNN

This paper is devoted to the investigation of the evaluation and query algorithm problem for the influence of spatial location based on RkNN(reverse k nearest neighbor).On the one hand,an object can make contribution to multiple locations.However,for the existing measures for evaluating the influence of spatial location,an object only makes contribution to one location,and its influence is usually measured by the number of spatial objects in the region.In this case,a new measure for evaluating the influence of spatial location based on the RkNN is proposed.Since the weight of the contribution is determined by the distance between the object and the location,the influence weight definition is given,which meets the actual applications.On the other hand,a query algorithm for the influence of spatial location is introduced based on the proposed measure.Firstly,an algorithm named INCH(INtersection’s Convex Hull)is applied to get candidate regions,where all objects are candidates.Then,kNN and Range-k are used to refine results.Then,according to the proposed measure,the weights of objects in RkNN results are computed,and the influence of the location is accumulated.The experimental results on the real data show that the optimized algorithms outperform the basic algorithm on efficiency.In addition,in order to provide the best customer service in the location problem and make the best use of all infrastructures,a location algorithm with the query is presented based on RkNN.The influence of each facility is calculated in the location program and the equilibrium coefficient is used to evaluate the reasonability of the location in the paper.The smaller the equilibrium coefficient is,the more reasonability the program is.The actual application shows that the location based on influence makes the location algorithm more reasonable and available.

Efficient Evaluation of Monitoring Top-t Most Influential Places

The continuous top-t most influential place （CTtMIP） query is defined formally and solved efficiently in this paper. A CTtMIP query continuously monitors the t places with the maximum influence from the set of places, where the influence of a place is defined as the number of its bichromatic reverse k nearest neighbors （BRkNNs）. Two new metrics and their corresponding rules are introduced to shrink the search region and reduce the candidates of BRkNNs checked. Extensive experiments confirm that our proposed approach outperforms the state-of-the-art competitor significantly.