Ranked Reverse Nearest Neighbor Search

Given a set of data points P and a query point q in a multidimensional space, reverse nearest neighbor (RNN) query finds data points in P whose nearest neighbors are q. Reverse k-nearest neighbor (RkNN) query (where k ges 1) generalizes RNN query to find data points whose kNNs include q. For RkNN query semantics, q is said to have influence to all those answer data points. The degree of q's influence on a data point p (isin P) is denoted by kappap where q is the kappap-th NN of p. We introduce a new variant of RNN query, namely, ranked reverse nearest neighbor (RRNN) query, that retrieves t data points most influenced by q, i.e., the t data points having the smallest kappa's with respect to q. To answer this RRNN query efficiently, we propose two novel algorithms, kappa-counting and kappa-browsing that are applicable to both monochromatic and bichromatic scenarios and are able to deliver results progressively. Through an extensive performance evaluation, we validate that the two proposed RRNN algorithms are superior to solutions derived from algorithms designed for RkNN query.     

Reverse Nearest Neighbor Search in Metric Spaces

Given a set {cal D} of objects, a reverse nearest neighbor (RNN) query returns the objects o in {cal D} such that o is closer to a query object q than to any other object in {cal D}, according to a certain similarity metric. The existing RNN solutions are not sufficient because they either 1) rely on precomputed information that is expensive to maintain in the presence of updates or 2) are applicable only when the data consists of "Euclidean objects” and similarity is measured using the L_2 norm. In this paper, we present the first algorithms for efficient RNN search in generic metric spaces. Our techniques require no detailed representations of objects, and can be applied as long as their mutual distances can be computed and the distance metric satisfies the triangle inequality. We confirm the effectiveness of the proposed methods with extensive experiments.     

Visible Reverse k-Nearest Neighbor Query Processing in Spatial Databases

Reverse nearest neighbor (RNN) queries have a broad application base such as decision support, profile-based marketing, resource allocation, etc. Previous work on RNN search does not take obstacles into consideration. In the real world, however, there are many physical obstacles (e.g., buildings) and their presence may affect the visibility between objects. In this paper, we introduce a novel variant of RNN queries, namely, visible reverse nearest neighbor (VRNN) search, which considers the impact of obstacles on the visibility of objects. Given a data set P, an obstacle set O, and a query point q in a 2D space, a VRNN query retrieves the points in P that have q as their visible nearest neighbor. We propose an efficient algorithm for VRNN query processing, assuming that P and O are indexed by R-trees. Our techniques do not require any preprocessing and employ half-plane property and visibility check to prune the search space. In addition, we extend our solution to several variations of VRNN queries, including: 1) visible reverse k-nearest neighbor (VRkNN) search, which finds the points in P that have q as one of their k visible nearest neighbors; 2) delta-VRkNN search, which handles VRkNN retrieval with the maximum visible distance delta constraint; and 3) constrained VRkNN (CVRkNN) search, which tackles the VRkNN query with region constraint. Extensive experiments on both real and synthetic data sets have been conducted to demonstrate the efficiency and effectiveness of our proposed algorithms under various experimental settings.     

路网中双色数据集上连续反向k近邻查询处理的研究

近年来,反向最近邻查询(RNN)算法研究得到了普遍的关注,成为了数据库领域的一个研究热点。欧氏空 间中提出了较多的高效算法,而路网中的反向最近邻处理方面所做的工作不够,有关这方面的成果较少。路网中查询 点和数据对象之间以及不同数据对象之间的距离受到路网连通性的影响,欧氏空间中的反向最近部方法在路网中不 适用。反向最近部查询有两种类型:单色反向最近部查询(Monochromatic RNN, MRNN)和双色反向最近部查询(13i- chromatic RNN,13RNN)。到目前为止,仍然没有有效的算法来处理路网中双色数据集上的连续反向k近部查询。因 此,研究路网中双色数据集上连续反向k近部查询是很有意义的。     

路网中互近邻查询处理方法

提出路网中的互近邻查询问题.给定路网G(V,E),对象集P,查询点q,近邻数k1和k2,互近邻查询返回既是q的k1近邻,又是q的反k2近邻的对象集.为解决该问题,首先提出基础算法,即先求出查询点q的k1近邻作为候选,再验证这些候选是否为真正的结果.然后,在此基础上提出了优化算法,根据落在对象点与查询点最短路径边上的标记点个数直接排除掉一些错误的候选对象.最后,通过实验验证了优化算法的有效性.     

Peer-to-peer bichromatic reverse nearest neighbours in mobile ad-hoc networks

The increasing use of mobile communications has raised many issues of decision support and resource allocation. A crucial problem is how to solve queries of Reverse Nearest Neighbour (RNN). An RNN query returns all objects that consider the query object as their nearest neighbour. Existing methods mostly rely on a centralised base station. However, mobile P2P systems offer many benefits, including self-organisation, fault-tolerance and load-balancing. In this study, we propose and evaluate 3 distinct P2P algorithms focusing on bichromatic RNN queries, in which mobile query peers and static objects of interest are of two different categories, based on a time-out mechanism and a boundary polygon around the mobile query peers. The Brute-Force Search Algorithm provides a naive approach to exploit shared information among peers whereas two other Boundary Search Algorithms filter a number of peers involved in query processing. The algorithms are evaluated in the MiXiM simulation framework with both real and synthetic datasets. The results show the practical feasibility of the P2P approach for solving bichromatic RNN queries for mobile networks.     

On multi-type reverse nearest neighbor search

This paper presents a study of the Multi-Type Reverse Nearest Neighbor (MTRNN) query problem. Traditionally, a reverse nearest neighbor (RNN) query finds all the objects that have the query point as their nearest neighbor. In contrast, an MTRNN query finds all the objects that have the query point in their multi-type nearest neighbors. Existing RNN queries find an influence set by considering only one feature type. However, the influence from multiple feature types is often critical for strategic decision making in many business scenarios, such as site selection for a new shopping center. To that end, we first formalize the notion of the MTRNN query by considering the influence of multiple feature types. We also propose R-tree based algorithms to find the influence set for a given query point and multiple feature types. Finally, experimental results are provided to show the strength of the proposed algorithms as well as design decisions related to performance tuning.     

Efficient processing of probabilistic reverse nearest neighbor queries over uncertain data

Reverse nearest neighbor (RNN) search is very crucial in many real applications. In particular, given a database and a query object, an RNN query retrieves all the data objects in the database that have the query object as their nearest neighbors. Often, due to limitation of measurement devices, environmental disturbance, or characteristics of applications (for example, monitoring moving objects), data obtained from the real world are uncertain (imprecise). Therefore, previous approaches proposed for answering an RNN query over exact (precise) database cannot be directly applied to the uncertain scenario. In this paper, we re-define the RNN query in the context of uncertain databases, namely probabilistic reverse nearest neighbor (PRNN) query, which obtains data objects with probabilities of being RNNs greater than or equal to a user-specified threshold. Since the retrieval of a PRNN query requires accessing all the objects in the database, which is quite costly, we also propose an effective pruning method, called geometric pruning (GP), that significantly reduces the PRNN search space yet without introducing any false dismissals. Furthermore, we present an efficient PRNN query procedure that seamlessly integrates our pruning method. Extensive experiments have demonstrated the efficiency and effectiveness of our proposed GP-based PRNN query processing approach, under various experimental settings.     

不确定数据上范围受限的最近邻查询算法

不确定数据的查询处理是数据库领域近年来的热点研究课题.提出一种不确定数据上的范围受限的最近邻查询.给定不确定数据集D={o1,o2,…,on},范围约束R是一个简单多边形,q为一固定的查询点,范围受限的最近邻查询返回的是在数据集D中,既满足范围约束R,又能成为查询点q的最近邻的对象集合.为处理该查询,提出了范围受限的最近邻核心集的概念和范围受限的最近邻核心集的查找算法.并提出一种计算范围受限的最近邻候选集的优化方法,降低了查询代价.最后通过实验验证了该算法的有效性.     

障碍环境中可视反向视域K最近邻查询

在障碍环境下的空间应用中,用户通常只对视域范围内可视的数据对象感兴趣。为解决障碍环境中视域范围内的反向最近邻查询问题,将视域可视性引入到反向K最近邻查询中,提出一种可视反向视域K最近邻查询算法。给定某空间数据集P、障碍集O和查询点q,可视反向视域K最近邻查询检索P中数据点,并将q作为可视视域K最近邻。应用查询点进行障碍过滤,得到障碍过滤算法,利用数据对象的视域进行剪枝,使用查询点与数据对象的关系剪枝,形成有效的障碍剪枝规则,并根据剪枝规则得到视域可视性判断算法。在此基础上,分别基于R^*-树和VFR-树提出可视反向视域K最近邻查询算法R^*-V2-RKNN和VFR-V2-RKNN,并分别通过对R^*-树和VFR-树进行一次遍历得到查询结果。在真实数据集和模拟数据集上的实验结果表明,VFR-V2-RKNN算法的查询性能明显优于R^*-V2-RKNN算法。     

Range nearest-neighbor query

A range nearest-neighbor (RNN) query retrieves the nearest neighbor (NN) for every point in a range. It is a natural generalization of point and continuous nearest-neighbor queries and has many applications. In this paper, we consider the ranges as (hyper)rectangles and propose efficient in-memory processing and secondary memory pruning techniques for RNN queries in both 2D and high-dimensional spaces. These techniques are generalized for kRNN queries, which return the k nearest neighbors for every point in the range. In addition, we devise an auxiliary solution-based index EXO-tree to speed up any type of NN query. EXO-tree is orthogonal to any existing NN processing algorithm and, thus, can be transparently integrated. An extensive empirical study was conducted to evaluate the CPU and I/O performance of these techniques, and the study showed that they are efficient and robust under various data sets, query ranges, numbers of nearest neighbors, dimensions, and cache sizes.     

基于Voronoi图的线段反向最近邻查询

提出一种基于平面线段的反向最近邻查询方法,用于找出线段集中以查询线段作为最近邻的线段。通过构造线段集的Voronoi图处理不相交的线段。根据其邻接特性和局部特性,给出基于Voronoi图的线段反向最近邻查询算法及相关定理和证明。实验结果表明,反向最近邻方法易于找到相交的线段,具有较高的查询效率。     

Optimal-Location-Selection Query Processing in Spatial Databases

This paper introduces and solves a novel type of spatial queries, namely, Optimal-Location-Selection (OLS) search, which has many applications in real life. Given a data object set D_A, a target object set D_B, a spatial region R, and a critical distance d_c in a multidimensional space, an OLS query retrieves those target objects in D_B that are outside R but have maximal optimality. Here, the optimality of a target object b in D_B located outside R is defined as the number of the data objects from D_A that are inside R and meanwhile have their distances to b not exceeding d_c. When there is a tie, the accumulated distance from the data objects to b serves as the tie breaker, and the one with smaller distance has the better optimality. In this paper, we present the optimality metric, formalize the OLS query, and propose several algorithms for processing OLS queries efficiently. A comprehensive experimental evaluation has been conducted using both real and synthetic data sets to demonstrate the efficiency and effectiveness of the proposed algorithms.     

Efficient mutual nearest neighbor query processing for moving object trajectories

Given a set D of trajectories, a query object q, and a query time extent Γ, a mutual (i.e., symmetric) nearest neighbor (MNN) query over trajectories finds from D, the set of trajectories that are among the k₁ nearest neighbors (NNs) of q within Γ, and meanwhile, have q as one of their k₂ NNs. This type of queries is useful in many applications such as decision making, data mining, and pattern recognition, as it considers both the proximity of the trajectories to q and the proximity of q to the trajectories. In this paper, we first formalize MNN search and identify its characteristics, and then develop several algorithms for processing MNN queries efficiently. In particular, we investigate two classes of MNN queries, i.e., MNN_P and MNN_T queries, which are defined with respect to stationary query points and moving query trajectories, respectively. Our methods utilize the batch processing and reusing technology to reduce the I/O cost (i.e., number of node/page accesses) and CPU time significantly. In addition, we extend our techniques to tackle historical continuous MNN (HCMNN) search for moving object trajectories, which returns the mutual nearest neighbors of q (for a specified k₁ and k₂) at any time instance of Γ. Extensive experiments with real and synthetic datasets demonstrate the performance of our proposed algorithms in terms of efficiency and scalability.     

Batch Nearest Neighbor Search for Video Retrieval

To retrieve similar videos to a query clip from a large database, each video is often represented by a sequence of high- dimensional feature vectors. Typically, given a query video containing m feature vectors, an independent nearest neighbor (NN) search for each feature vector is often first performed. After completing all the NN searches, an overall similarity is then computed, i.e., a single content-based video retrieval usually involves m individual NN searches. Since normally nearby feature vectors in a video are similar, a large number of expensive random disk accesses are expected to repeatedly occur, which crucially affects the overall query performance. Batch nearest neighbor (BNN) search is stated as a batch operation that performs a number of individual NN searches. This paper presents a novel approach towards efficient high-dimensional BNN search called dynamic query ordering (DQO) for advanced optimizations of both I/O and CPU costs. Observing the overlapped candidates (or search space) of a pervious query may help to further reduce the candidate sets of subsequent queries, DQO aims at progressively finding a query order such that the common candidates among queries are fully utilized to maximally reduce the total number of candidates. Modelling the candidate set relationship of queries by a candidate overlapping graph (COG), DQO iteratively selects the next query to be executed based on its estimated pruning power to the rest of queries with the dynamically updated COG. Extensive experiments are conducted on real video datasets and show the significance of our BNN query processing strategy.     

受限网络模糊对象最近邻查询

针对网络空间中有范围约束、不确定对象的最近邻查询问题,提出范围受限的网络空间模糊对象最近邻查询概念,并根据查询顺序的不同,给出NN-R查询算法和R-NN查询算法。两种算法均采用网络位置信息与连接信息分别存储的方式,使用聚类文件进行组织,减少I/O操作。NN-R算法在近邻查询过程中利用查询对象与受限范围的α-距离作为约束,缩小搜索范围。R-NN算法将受限范围内查询对象的欧氏近邻作为候选对象,利用欧氏距离的下界性与易求性降低时间复杂度。两种算法时间复杂度分别为O((log_(m1)|E|+(|V~*|m3+1)log_(m2)|V|+|E|+|V|log|V|+n(lgn+1))和O(log_(m4)n+(k+1)log_(m1)|E|+|E|+|V|log|V|)。实验结果表明,在各自适用条件下,两种算法均有较好的性能。     

K-nearest neighbor finding using MaxNearestDist

Similarity searching often reduces to finding the k nearest neighbors to a query object. Finding the k nearest neighbors is achieved by applying either a depth- first or a best-first algorithm to the search hierarchy containing the data. These algorithms are generally applicable to any index based on hierarchical clustering. The idea is that the data is partitioned into clusters which are aggregated to form other clusters, with the total aggregation being represented as a tree. These algorithms have traditionally used a lower bound corresponding to the minimum distance at which a nearest neighbor can be found (termed MinDist) to prune the search process by avoiding the processing of some of the clusters as well as individual objects when they can be shown to be farther from the query object q than all of the current k nearest neighbors of q. An alternative pruning technique that uses an upper bound corresponding to the maximum possible distance at which a nearest neighbor is guaranteed to be found (termed MaxNearestDist) is described. The MaxNearestDist upper bound is adapted to enable its use for finding the k nearest neighbors instead of just the nearest neighbor (i.e., k=1) as in its previous uses. Both the depth-first and best-first k-nearest neighbor algorithms are modified to use MaxNearestDist, which is shown to enhance both algorithms by overcoming their shortcomings. In particular, for the depth-first algorithm, the number of clusters in the search hierarchy that must be examined is not increased thereby potentially lowering its execution time, while for the best-first algorithm, the number of clusters in the search hierarchy that must be retained in the priority queue used to control the ordering of processing of the clusters is also not increased, thereby potentially lowering its storage requirements.     

面向移动对象的高效组最近邻居查询方法

组最近邻居查询是移动对象数据库重要的查询类型之一。本文提出了一种基于网格索引结构的剪枝搜索策略,将空间区域划分为网格,通过对象点的网格单元标识减少组最近邻居查询所需要的节点访问代价。用步长迭代法得到查询对象集的质心,提出了一种移动对象组最近邻居查询MOGNN算法,采用更精确的裁剪搜索空间准则,减少了查询所需要访问的节点数目。实验结果与分析表明,基于网格索引的MOGNN查询算法具有良好的查询性能。     

Efficient KNN search by linear projection of image clusters

K‐nearest neighbors (KNN) search in a high‐dimensional vector space is an important paradigm for a variety of applications. Despite the continuous efforts in the past years, algorithms to find the exact KNN answer set at high dimensions are outperformed by a linear scan method. In this paper, we propose a technique to find the exact KNN image objects to a given query object. First, the proposed technique clusters the images using a self‐organizing map algorithm and then it projects the found clusters into points in a linear space based on the distances between each cluster and a selected reference point. These projected points are then organized in a simple, compact, and yet fast index structure called array‐index. Unlike most indexes that support KNN search, the array‐index requires a storage space that is linear in the number of projected points. The experiments show that the proposed technique is more efficient and robust to dimensionality as compared to other well‐known techniques because of its simplicity and compactness. © 2011 Wiley Periodicals, Inc.     

Optimal location query based on k nearest neighbours

Optimal location query in road networks is a basic operation in the location intelligence applications. Given a set of clients and servers on a road network, the purpose of optimal location query is to obtain a location for a new server, so that a certain objective function calculated based on the locations of clients and servers is optimal. Existing works assume no labels for servers and that a client only visits the nearest server. These assumptions are not realistic and it renders the existing work not useful in many cases. In this paper, we relax these assumptions and consider the k nearest neighbours (KNN) of clients. We introduce the problem of KNN-based optimal location query (KOLQ) which considers the k nearest servers of clients and labeled servers. We also introduce a variant problem called relocation KOLQ (RKOLQ) which aims at relocating an existing server to an optimal location. Two main analysis algorithms are proposed for these problems. Extensive experiments on the real road networks illustrate the efficiency of our proposed solutions.