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.     

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。     

RASIM: a rank-aware separate index method for answering top-k spatial keyword queries

A top-k spatial keyword query returns k objects having the highest (or lowest) scores with regard to spatial proximity as well as text relevancy. Approaches for answering top-k spatial keyword queries can be classified into two categories: the separate index approach and the hybrid index approach. The separate index approach maintains the spatial index and the text index independently and can accommodate new data types. However, it is difficult to support top-k pruning and merging efficiently at the same time since it requires two different orders for clustering the objects: the first based on scores for top-k pruning and the second based on object IDs for efficient merging. In this paper, we propose a new separate index method called Rank-Aware Separate Index Method (RASIM) for top-k spatial keyword queries. RASIM supports both top-k pruning and efficient merging at the same time by clustering each separate index in two different orders through the partitioning technique. Specifically, RASIM partitions the set of objects in each index into rank-aware (RA) groups that contain the objects with similar scores and applies the first order to these groups according to their scores and the second order to the objects within each group according to their object IDs. Based on the RA groups, we propose two query processing algorithms: (i) External Threshold Algorithm (External TA) that supports top-k pruning in the unit of RA groups and (ii) Generalized External TA that enhances the performance of External TA by exploiting special properties of the RA groups. RASIM is the first research work that supports top-k pruning based on the separate index approach. Naturally, it keeps the advantages of the separate index approach. In addition, in terms of storage and query processing time, RASIM is more efficient than the IR-tree method, which is the prevailing method to support top-k pruning to date and is based on the hybrid index approach. Experimental results show that, compared with the IR-tree method, the index size of RASIM is reduced by up to 1.85 times, and the query performance is improved by up to 3.22 times.     

Continuous visible k nearest neighbor query on moving objects

A visible k nearest neighbor (Vk NN) query retrieves k objects that are visible and nearest to the query object, where “visible” means that there is no obstacle between an object and the query object. Existing studies on the Vk NN query have focused on static data objects. In this paper we investigate how to process the query on moving objects continuously. We propose an effective filtering-and-refinement framework for evaluating this type of queries. We exploit spatial proximity and visibility properties between the query object and data objects to prune search space under this framework. A detailed cost analysis and a comprehensive experimental study are conducted on the proposed framework. The results validate the effectiveness of the pruning techniques and verify the efficiency of the proposed framework. The proposed framework outperforms a straightforward solution by an order of magnitude in terms of both communication and computation costs.     

Answering why-not and why questions on reverse top-<Emphasis Type="Italic">k</Emphasis> queries

Why-not and why questions can be posed by database users to seek clarifications on unexpected query results. Specifically, why-not questions aim to explain why certain expected tuples are absent from the query results, while why questions try to clarify why certain unexpected tuples are present in the query results. This paper systematically explores the why-not and why questions on reverse top-k queries, owing to its importance in multi-criteria decision making. We first formalize why-not questions on reverse top-k queries, which try to include the missing objects in the reverse top-k query results, and then, we propose a unified framework called WQRTQ to answer why-not questions on reverse top-k queries. Our framework offers three solutions to cater for different application scenarios. Furthermore, we study why questions on reverse top-k queries, which aim to exclude the undesirable objects from the reverse top-k query results, and extend the framework WQRTQ to efficiently answer why questions on reverse top-k queries, which demonstrates the flexibility of our proposed algorithms. Extensive experimental evaluation with both real and synthetic data sets verifies the effectiveness and efficiency of the presented algorithms under various experimental settings.     

室内概率阈值反向最近邻查询

室内空间变得越发的庞大和复杂,随之产生了越来越多的室内空间查询需求.目前已有文献提出了针对室内空间环境的范围查询和最近邻查询,而作为常见的空间查询类型的反向最近邻查询,尚未有相关的研究.为此,提出了室内概率阈值反向最近邻查询和基于定位设备的设备可达图模型.在图模型基础上,提出了室内概率阈值反向最近邻查询处理算法,该算法由基于图模型的批量剪枝、基于室内距离的剪枝、基于概率的剪枝和概率计算4部分构成,通过剪枝策略修剪掉不可能出现在结果集中的对象,从而缩小了查询空间,提高了效率.     

Spatial inverse query processing

Traditional spatial queries return, for a given query object q, all database objects that satisfy a given predicate, such as epsilon range and k-nearest neighbors. This paper defines and studies inverse spatial queries, which, given a subset of database objects Q and a query predicate, return all objects which, if used as query objects with the predicate, contain Q in their result. We first show a straightforward solution for answering inverse spatial queries for any query predicate. Then, we propose a filter-and-refinement framework that can be used to improve efficiency. We show how to apply this framework on a variety of inverse queries, using appropriate space pruning strategies. In particular, we propose solutions for inverse epsilon range queries, inverse k-nearest neighbor queries, and inverse skyline queries. Furthermore, we show how to relax the definition of inverse queries in order to ensure non-empty result sets. Our experiments show that our framework is significantly more efficient than naive approaches.     

Top-n query processing in spatial databases considering bi-chromatic reverse k-nearest neighbors

A reverse k-nearest neighbor (RkNN) query retrieves the data points which regard the query point as one of their respective k nearest neighbors. A bi-chromatic reverse k-nearest neighbor (BRkNN) query is a variant of the RkNN query, considering two types of data. Given two types of data G and C, a BRkNN query regarding a data point q in G retrieves the data points from C that regard q as one of their respective k-nearest neighbors among the data points in G. Many existing approaches answer either the RkNN query or the BRkNN query. Different from these approaches, in this paper, we make the first attempt to propose a top-n query based on the concept of BRkNN queries, which ranks the data points in G and retrieves the top-n points according to the cardinalities of the corresponding BRkNN answer sets. For efficiently answering this top-n query, we construct the Voronoi Diagram of G to index the data points in G and C. From the information associated with the Voronoi Diagram of G, the upper bound of the cardinality of the BRkNN answer sets for each data point in G can be quickly computed. Moreover, based on an existing approach to answering the RkNN query and the characteristics of the Voronoi Diagram of G, we propose a method to find the candidate region regarding a BRkNN query, which tightens the corresponding search space. Finally, based on the triangle inequality, we propose an efficient refinement algorithm for finding the exact BRkNN answers from the candidate regions. To evaluate our approach on answering the top-n query, it is compared with an approach which applies a state-of-the-art algorithm for answering the BRkNN query to each data point in G. The experiment results reveal that our approach has a much better performance.     

Continuous reverse k nearest neighbors queries in Euclidean space and in spatial networks

In this paper, we study the problem of continuous monitoring of reverse k nearest neighbors queries in Euclidean space as well as in spatial networks. Existing techniques are sensitive toward objects and queries movement. For example, the results of a query are to be recomputed whenever the query changes its location. We present a framework for continuous reverse k nearest neighbor (RkNN) queries by assigning each object and query with a safe region such that the expensive recomputation is not required as long as the query and objects remain in their respective safe regions. This significantly improves the computation cost. As a byproduct, our framework also reduces the communication cost in client–server architectures because an object does not report its location to the server unless it leaves its safe region or the server sends a location update request. We also conduct a rigid cost analysis for our Euclidean space RkNN algorithm. We show that our techniques can also be applied to answer bichromatic RkNN queries in Euclidean space as well as in spatial networks. Furthermore, we show that our techniques can be extended for the spatial networks that are represented by directed graphs. The extensive experiments demonstrate that our techniques outperform the existing techniques by an order of magnitude in terms of computation cost and communication cost.     

Efficiently processing snapshot and continuous reverse k nearest neighbors queries

Given a set of objects and a query q, a point p is called the reverse k nearest neighbor (RkNN) of q if q is one of the k closest objects of p. In this paper, we introduce the concept of influence zone that is the area such that every point inside this area is the RkNN of q and every point outside this area is not the RkNN. The influence zone has several applications in location-based services, marketing and decision support systems. It can also be used to efficiently process RkNN queries. First, we present efficient algorithm to compute the influence zone. Then, based on the influence zone, we present efficient algorithms to process RkNN queries that significantly outperform existing best-known techniques for both the snapshot and continuous RkNN queries. We also present a detailed theoretical analysis to analyze the area of the influence zone and IO costs of our RkNN processing algorithms. Our experiments demonstrate the accuracy of our theoretical analysis. This paper is an extended version of our previous work (Cheema et?al. in Proceedings of ICDE, pp. 577–588, 2011). We make the following new contributions in this extended version: (1) we conduct a rigorous complexity analysis and show that the complexity of one of our proposed algorithms in Cheema et?al. (Proceedings of ICDE, pp. 577–588, 2011) can be reduced from O(m ²) to O( km) where m?>?k is the number of objects used to compute the influence zone, (2) we show that our techniques can be applied to dimensionality higher than two, and (3) we present efficient techniques to handle data updates.     

Probabilistic Group Nearest Neighbor Queries in Uncertain Databases

The importance of query processing over uncertain data has recently arisen due to its wide usage in many real-world applications. In the context of uncertain databases, previous works have studied many query types such as nearest neighbor query, range query, top-k query, skyline query, and similarity join. In this paper, we focus on another important query, namely, probabilistic group nearest neighbor (PGNN) query, in the uncertain database, which also has many applications. Specifically, given a set, Q, of query points, a PGNN query retrieves data objects that minimize the aggregate distance (e.g., sum, min, and max) to query set Q. Due to the inherent uncertainty of data objects, previous techniques to answer group nearest neighbor (GNN) query cannot be directly applied to our PGNN problem. Motivated by this, we propose effective pruning methods, namely, spatial pruning and probabilistic pruning, to reduce the PGNN search space, which can be seamlessly integrated into our PGNN query procedure. Extensive experiments have demonstrated the efficiency and effectiveness of our proposed approach, in terms of the wall clock time and the speed-up ratio against linear scan.     

Approximate Continuous Top-<Emphasis Type="Italic">k</Emphasis> Query over Sliding Window

Continuous top-k query over sliding window is a fundamental problem in database, which retrieves k objects with the highest scores when the window slides. Existing studies mainly adopt exact algorithms to tackle this type of queries, whose key idea is to maintain a subset of objects in the window, and try to retrieve answers from it. However, all the existing algorithms are sensitive to query parameters and data distribution. In addition, they suffer from expensive overhead for incremental maintenance, and thus cannot satisfy real-time requirement. In this paper, we define a novel query named (ε, δ)-approximate continuous top-k query, which returns approximate answers for top-k query. In order to efficiently support this query, we propose an efficient framework, named PABF (Probabilistic Approximate Based Framework), to support approximate top-k query over sliding window. We firstly maintain a self-adaptive pruning value, which could filter out newly arrived objects who have a probability less than 1 ? δ of being a query result. For those objects that are not filtered, we combine them together, if the score difference among them is less than a threshold. To efficiently maintain these combined results, the framework PABF also proposes a multi-phase merging algorithm. Theoretical analysis indicates that even in the worst case, we require only logarithmic complexity for maintaining each candidate.     

基于空间网络数据库的组最近邻居查询

组最近邻居查询是空间数据库在最近邻居查询上的新问题.目前,对组最近邻居查询的研究局限于欧氏空间,考察的只是对象间的相对位置关系,无法处理现实生活中对象间的连通性问题.鉴于此,本文基于空间网络数据库提出以网络距离为度量标准的组最近邻居查询概念,进而提出作为其算法基础的增量最近邻居查询算法INNN,最后构造出算法NMQM.
实验证明,NMQM是一种有效的组最近邻居查询算法.     

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 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.     

Continuous visible nearest neighbor query processing in spatial databases

In this paper, we identify and solve a new type of spatial queries, called continuous visible nearest neighbor (CVNN) search. Given a data set P, an obstacle set O, and a query line segment q in a two-dimensional space, a CVNN query returns a set of \({\langle p, R\rangle}\) tuples such that \({p \in P}\) is the nearest neighbor to every point r along the interval \({R \subseteq q}\) as well as p is visible to r. Note that p may be NULL, meaning that all points in P are invisible to all points in R due to the obstruction of some obstacles in O. In contrast to existing continuous nearest neighbor query, CVNN retrieval considers the impact of obstacles on visibility between objects, which is ignored by most of spatial queries. We formulate the problem, analyze its unique characteristics, and develop efficient algorithms for exact CVNN query processing. Our methods (1) utilize conventional data-partitioning indices (e.g., R-trees) on both P and O, (2) tackle the CVNN search by performing a single query for the entire query line segment, and (3) only access the data points and obstacles relevant to the final query result by employing a suite of effective pruning heuristics. In addition, several interesting variations of CVNN queries have been introduced, and they can be supported by our techniques, which further demonstrates the flexibility of the proposed algorithms. A comprehensive experimental evaluation using both real and synthetic data sets has been conducted to verify the effectiveness of our proposed pruning heuristics and the performance of our proposed algorithms.     

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.     

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.     

Continuous reverse k nearest neighbor monitoring on moving objects in road networks

Continuous reverse k nearest neighbor (CRkNN) monitoring in road networks has recently received increasing attentions. However, there is still a lack of efficient CRkNN algorithms in road networks up to now. In road networks, moving query objects and data objects are restricted by the connectivity of the road network and both the object–query distance and object–object distance updates affect the result of CRkNN queries. In this paper, we present a novel algorithm for continuous and incremental evaluation of CRkNN queries in road networks. Our method is based on a novel data structure called dual layer multiway tree (DLM tree) we proposed to represent the whole monitoring region of a CRkNN query q. We propose several lemmas to reduce the monitoring region of q and the number of candidate objects as much as possible. Moreover, by associating a variable NN_count with each candidate object, we can simplify the monitoring of candidate objects. There are a large number of objects roaming in a road network and many of them are irrelevant to a specific CRkNN query of a query object q. To minimize the processing extension, for a road in the network, we give an IQL list and an IQCL list to specify the set of query objects and data objects whose location updates should be maintained for CRkNN processing of query objects. Our CRkNN method consists of two phase: the initial result generating phase and incremental maintenance phase. In each phase, algorithms with high performance are proposed to make our CRkNN method more efficient. Extensive simulation experiments are conducted and the result shows that our proposed approach is efficient and scalable in processing CRkNN queries in road networks.     

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.