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.     

The direction-constrained <Emphasis Type="Italic">k</Emphasis> nearest neighbor query

Finding k nearest neighbor objects in spatial databases is a fundamental problem in many geospatial systems and the direction is one of the key features of a spatial object. Moreover, the recent tremendous growth of sensor technologies in mobile devices produces an enormous amount of spatio-directional (i.e., spatially and directionally encoded) objects such as photos. Therefore, an efficient and proper utilization of the direction feature is a new challenge. Inspired by this issue and the traditional k nearest neighbor search problem, we devise a new type of query, called the direction-constrained k nearest neighbor (DCkNN) query. The DCkNN query finds k nearest neighbors from the location of the query such that the direction of each neighbor is in a certain range from the direction of the query. We develop a new index structure called MULTI, to efficiently answer the DCkNN query with two novel index access algorithms based on the cost analysis. Furthermore, our problem and solution can be generalized to deal with spatio-circulant dimensional (such as a direction and circulant periods of time such as an hour, a day, and a week) objects. Experimental results show that our proposed index structure and access algorithms outperform two adapted algorithms from existing kNN algorithms.     

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.     

Reverse nearest neighbors in large graphs

A reverse nearest neighbor (RNN) query returns the data objects that have a query point as their nearest neighbor (NN). Although such queries have been studied quite extensively in Euclidean spaces, there is no previous work in the context of large graphs. In this paper, we provide a fundamental lemma, which can be used to prune the search space while traversing the graph in search for RNN. Based on it, we develop two RNN methods; an eager algorithm that attempts to prune network nodes as soon as they are visited and a lazy technique that prunes the search space when a data point is discovered. We study retrieval of an arbitrary number k of reverse nearest neighbors, investigate the benefits of materialization, cover several query types, and deal with cases where the queries and the data objects reside on nodes or edges of the graph. The proposed techniques are evaluated in various practical scenarios involving spatial maps, computer networks, and the DBLP coauthorship graph.     

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。     

使用R树进行k-NN搜索

在地理信息系统中经常要做k-NN搜索，进行这些查询用到的算法与位置和范围查询的算法不同，需要专门进行研究，介绍了一种分支界限遍历R树算法，并将该算法概括为k-NN算法。文中讨论了两种方法。对R树进行结点内MBR的排序以及剪枝过程，以减少搜索空间中需访问结点的数量，有效地进行k-NN搜索。     

Reverse Nearest Neighbors Search in Ad Hoc Subspaces

Given an object q, modeled by a multidimensional point, a reverse nearest neighbors (RNN) query returns the set of objects in the database that have q as their nearest neighbor. In this paper, we study an interesting generalization of the RNN query, where not all dimensions are considered, but only an ad hoc subset thereof. The rationale is that 1) the dimensionality might be too high for the result of a regular RNN query to be useful, 2) missing values may implicitly define a meaningful subspace for RNN retrieval, and 3) analysts may be interested in the query results only for a set of (ad hoc) problem dimensions (i.e., object attributes). We consider a suitable storage scheme and develop appropriate algorithms for projected RNN queries, without relying on multidimensional indexes. Given the significant cost difference between random and sequential data accesses, our algorithms are based on applying sequential accesses only on the projected atomic values of the data at each dimension, to progressively derive a set of RNN candidates. Whether these candidates are actual RNN results is then validated via an optimized refinement step. In addition, we study variants of the projected RNN problem, including RkNN search, bichromatic RNN, and RNN retrieval for the case where sequential accesses are not possible. Our methods are experimentally evaluated with real and synthetic data     

Nearest and reverse nearest neighbor queries for moving objects

With the continued proliferation of wireless communications and advances in positioning technologies, algorithms for efficiently answering queries about large populations of moving objects are gaining interest. This paper proposes algorithms for k nearest and reverse k nearest neighbor queries on the current and anticipated future positions of points moving continuously in the plane. The former type of query returns k objects nearest to a query object for each time point during a time interval, while the latter returns the objects that have a specified query object as one of their k closest neighbors, again for each time point during a time interval. In addition, algorithms for so-called persistent and continuous variants of these queries are provided. The algorithms are based on the indexing of object positions represented as linear functions of time. The results of empirical performance experiments are reported.     

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.     

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.     

Unified framework for representing and ranking

In the database retrieval and nearest neighbor classification tasks, the two basic problems are to represent the query and database objects, and to learn the ranking scores of the database objects to the query. Many studies have been conducted for the representation learning and the ranking score learning problems, however, they are always learned independently from each other. In this paper, we argue that there are some inner relationships between the representation and ranking of database objects, and try to investigate their relationships by learning them in a unified way. To this end, we proposed the Unified framework for Representation and Ranking (UR²) of objects for the database retrieval and nearest neighbor classification tasks. The learning of representation parameter and the ranking scores are modeled within one single unified objective function. The objective function is optimized alternately with regard to representation parameter and the ranking scores. Based on the optimization results, iterative algorithms are developed to learn the representation parameter and the ranking scores on a unified way. Moreover, with two different formulas of representation (feature selection and subspace learning), we give two versions of UR². The proposed algorithms are tested on two challenging tasks – MRI image based brain tumor retrieval and nearest neighbor classification based protein identification. The experiments show the advantage of the proposed unified framework over the state-of-the-art independent representation and ranking methods.     

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。     

Efficient moving <Emphasis Type="Italic">k</Emphasis> nearest neighbor queries over line segment objects

The growing need for location based services motivates the moving k nearest neighbor query (MkNN), which requires to find the k nearest neighbors of a moving query point continuously. In most existing solutions, data objects are abstracted as points. However, lots of real-world data objects, such as roads, rivers or pipelines, should be reasonably modeled as line segments or polyline segments. In this paper, we present LV*-Diagram to handle MkNN queries over line segment data objects. LV*-Diagram dynamically constructs a safe region. The query results remain unchanged if the query point is in the safe region, and hence, the computation cost of the server is greatly reduced. Experimental results show that our approach significantly outperforms the baseline method w.r.t. CPU load, I/O, and communication costs.     

时空数据库中多个最近邻对象的查询算法

在时空数据库中，最近邻查询用于对某个查询对象，在被查询对象中找出离它最近的一个或多个对象。该文在TPR树这一时空索引的基础上，提出了一种高效的最近邻查询算法，能够支持移动对象的多个最近邻对象的查询，并在性能上也有所提高。     

Optimized algorithms for predictive range and KNN queries on moving objects

There have been many studies on management of moving objects recently. Most of them try to optimize the performance of predictive window queries. However, not much attention is paid to two other important query types: the predictive range query and the predictive k nearest neighbor query. In this article, we focus on these two types of queries. The novelty of our work mainly lies in the introduction of the Transformed Minkowski Sum, which can be used to determine whether a moving bounding rectangle intersects a moving circular query region. This enables us to use the traditional tree traversal algorithms to perform range and kNN searches. We theoretically show that our algorithms based on the Transformed Minkowski Sum are optimal in terms of the number of tree node accesses. We also experimentally verify the effectiveness of our technique and show that our algorithms outperform alternative approaches.     

DART+: Direction-aware bichromatic reverse k nearest neighbor query processing in spatial databases

This article presents a novel type of queries in spatial databases, called the direction-aware bichromatic reverse k nearest neighbor(DBRkNN) queries, which extend the bichromatic reverse nearest neighbor queries. Given two disjoint sets, P and S, of spatial objects, and a query object q in S, the DBRkNN query returns a subset P′ of P such that k nearest neighbors of each object in P′ include q and each object in P′ has a direction toward q within a pre-defined distance. We formally define the DBRkNN query, and then propose an efficient algorithm, called DART, for processing the DBRkNN query. Our method utilizes a grid-based index to cluster the spatial objects, and the B⁺-tree to index the direction angle. We adopt a filter-refinement framework that is widely used in many algorithms for reverse nearest neighbor queries. In the filtering step, DART eliminates all the objects that are away from the query object more than a pre-defined distance, or have an invalid direction angle. In the refinement step, remaining objects are verified whether the query object is actually one of the k nearest neighbors of them. As a major extension of DART, we also present an improved algorithm, called DART+, for DBRkNN queries. From extensive experiments with several datasets, we show that DART outperforms an R-tree-based naive algorithm in both indexing time and query processing time. In addition, our extension algorithm, DART+, also shows significantly better performance than DART.     

Direction-aware KNN queries for moving objects in a road network

Recently more and more people focus on k-nearest neighbor (KNN) query processing over moving objects in road networks, e.g., taxi hailing and ride sharing. However, as far as we know, the existing k-nearest neighbor (KNN) queries take distance as the major criteria for nearest neighbor objects, even without taking direction into consideration. The main issue with existing methods is that moving objects change their locations and directions frequently over time, so the information updates cannot be processed in time and they run the risk of retrieving the incorrect KNN results. They may fail to meet users’ needs in certain scenarios, especially in the case of querying k-nearest neighbors for moving objects in a road network. In order to find the top k-nearest objects moving toward a query point, this paper presents a novel algorithm for direction-aware KNN (DAKNN) queries for moving objects in a road network. In this method, R-tree and simple grid are firstly used as the underlying index structure, where the R-tree is used for indexing the static road network and the simple grid is used for indexing the moving objects. Then, it introduces the notion of “azimuth” to represent the moving direction of objects in a road network, and presents a novel local network expansion method to quickly judge the direction of the moving objects. By considering whether a moving object is moving farther away from or getting closer to a query point, the object that is definitely not in the KNN result set is effectively excluded. Thus, we can reduce the communication cost, meanwhile simplify the computation of moving direction between moving objects and query point. Comprehensive experiments are conducted and the results show that our algorithm can achieve real-time and efficient queries in retrieving objects moving toward query point in a road network.

     

Continuous aggregate nearest neighbor queries

This paper addresses the problem of continuous aggregate nearest-neighbor (CANN) queries for moving objects in spatio-temporal data stream management systems. A CANN query specifies a set of landmarks, an integer k, and an aggregate distance function f (e.g., min, max, or sum), where f computes the aggregate distance between a moving object and each of the landmarks. The answer to this continuous query is the set of k moving objects that have the smallest aggregate distance f. A CANN query may also be viewed as a combined set of nearest neighbor queries. We introduce several algorithms to continuously and incrementally answer CANN queries. Extensive experimentation shows that the proposed operators outperform the state-of-the-art algorithms by up to a factor of 3 and incur low memory overhead.     

移动对象的动态反向k最近邻研究

反向最近邻查询是空间数据库中最重要的算法之一。传统的反向最近邻查询方法主要是针对静态对象的查询,随着无线通讯和定位技术的快速发展,移动对象发出的查询请求成为新的研究热点。该文将TPR-tree作为算法的索引结构,并提出了基于矩形框的对角线的修剪策略,将半平面修剪策略进行改进,给出了移动对象的动态反向k最近邻的查询方案。     

Spatial query processing for fuzzy objects

Range and nearest neighbor queries are the most common types of spatial queries, which have been investigated extensively in the last decades due to its broad range of applications. In this paper, we study this problem in the context of fuzzy objects that have indeterministic boundaries. Fuzzy objects play an important role in many areas, such as biomedical image databases and GIS communities. Existing research on fuzzy objects mainly focuses on modeling basic fuzzy object types and operations, leaving the processing of more advanced queries largely untouched. In this paper, we propose two new kinds of spatial queries for fuzzy objects, namely single threshold query and continuous threshold query, to determine the query results which qualify at a certain probability threshold and within a probability interval, respectively. For efficient single threshold query processing, we optimize the classical R-tree-based search algorithm by deriving more accurate approximations for the distance function between fuzzy objects and the query object. To enhance the performance of continuous threshold queries, effective pruning rules are developed to reduce the search space and speed up the candidate refinement process. The efficiency of our proposed algorithms as well as the optimization techniques is verified with an extensive set of experiments using both synthetic and real datasets.