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.     

Monochromatic and bichromatic reverse top-k group nearest neighbor queries

The Group Nearest Neighbor (GNN) search is an important approach for expert and intelligent systems, i.e., Geographic Information System (GIS) and Decision Support System (DSS). However, traditional GNN search starts from users’ perspective and selects the locations or objects that users like. Such applications fail to help the managers since they do not provide managerial insights. In this paper, we focus on solving the problem from the managers’ perspective. In particular, we propose a novel GNN query, namely, the reverse top-k group nearest neighbor (RkGNN) query which returns k groups of data objects so that each group has the query object q as their group nearest neighbor (GNN). This query is an important tool for decision support, e.g., location-based service, product data analysis, trip planning, and disaster management because it provides data analysts an intuitive way for finding significant groups of data objects with respect to q. Despite their importance, this kind of queries has not received adequate attention from the research community and it is a challenging task to efficiently answer the RkGNN queries. To this end, we first formalize the reverse top-k group nearest neighbor query in both monochromatic and bichromatic cases, and then propose effective pruning methods, i.e., sorting and threshold pruning, MBR property pruning, and window pruning, to reduce the search space during the RkGNN query processing. Furthermore, we improve the performance by employing the reuse heap technique. As an extension to the RkGNN query, we also study an interesting variant of the RkGNN query, namely a constrained reverse top-k group nearest neighbor (CRkGN) query. Extensive experiments using synthetic and real datasets demonstrate the efficiency and effectiveness of our approaches.     

Algorithms for constrained <Emphasis Type="Italic">k</Emphasis>-nearest neighbor queries over moving object trajectories

An important query for spatio-temporal databases is to find nearest trajectories of moving objects. Existing work on this topic focuses on the closest trajectories in the whole data space. In this paper, we introduce and solve constrained k-nearest neighbor (CkNN) queries and historical continuous CkNN (HCCkNN) queries on R-tree-like structures storing historical information about moving object trajectories. Given a trajectory set D, a query object (point or trajectory) q, a temporal extent T, and a constrained region CR, (i) a CkNN query over trajectories retrieves from D within T, the k (≥ 1) trajectories that lie closest to q and intersect (or are enclosed by) CR; and (ii) an HCCkNN query on trajectories retrieves the constrained k nearest neighbors (CkNNs) of q at any time instance of T. We propose a suite of algorithms for processing CkNN queries and HCCkNN queries respectively, with different properties and advantages. In particular, we thoroughly investigate two types of CkNN queries, i.e., CkNN_P and CkNN_T, which are defined with respect to stationary query points and moving query trajectories, respectively; and two types of HCCkNN queries, namely, HCCkNN_P and HCCkNN_T, which are continuous counterparts of CkNN_P and CkNN_T, respectively. Our methods utilize an existing data-partitioning index for trajectory data (i.e., TB-tree) to achieve low I/O and CPU cost. Extensive experiments with both real and synthetic datasets demonstrate the performance of the proposed algorithms in terms of efficiency and scalability.     

Monochromatic and bichromatic ranked reverse boolean spatial keyword nearest neighbors search

Recently, Reverse k Nearest Neighbors (RkNN) queries, returning every answer for which the query is one of its k nearest neighbors, have been extensively studied on the database research community. But the RkNN query cannot retrieve spatio-textual objects which are described by their spatial location and a set of keywords. Therefore, researchers proposed a RSTkNN query to find these objects, taking both spatial and textual similarity into consideration. However, the RSTkNN query cannot control the size of answer set and to be sorted according to the degree of influence on the query. In this paper, we propose a new problem Ranked Reverse Boolean Spatial Keyword Nearest Neighbors query called Ranked-RBSKNN query, which considers both spatial similarity and textual relevance, and returns t answers with most degree of influence. We propose a separate index and a hybrid index to process such queries efficiently. Experimental results on different real-world and synthetic datasets show that our approaches achieve better performance.     

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.     

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 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.     

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.     

面向移动对象连续k近邻查询的双层索引结构

移动对象连续k近邻（CKNN）查询是指给定一个连续移动的对象集合,对于任意一个k近邻查询q,实时计算查询q的k近邻并在查询有效时间内对查询结果进行实时更新.现实生活中,交通出行、社交网络、电子商务等领域许多基于位置的应用服务都涉及移动对象连续k近邻查询这一基础问题.已有研究工作解决连续k近邻查询问题时,大多需要通过多次迭代确定一个包含k近邻的查询范围,而每次迭代需要根据移动对象的位置计算当前查询范围内移动对象的数量,整个迭代过程的计算代价占查询代价的很大部分.为此,提出了一种基于网络索引和混合高斯函数移动对象分布密度的双重索引结构（grid GMM index,GGI）,并设计了移动对象连续k近邻增量查询算法（incremental search for continuous k nearest neighbors,IS-CKNN）.GGI索引结构的底层采用网格索引对海量移动对象进行维护,上层构建混合高斯模型模拟移动对象在二维空间中的分布.对于给定的k近邻查询q,IS-CKNN算法能够基于混合高斯模型直接确定一个包含q的k近邻的查询区域,减少了已有算法求解该区域的多次迭代过程;当移动对象和查询q位置发生变化时,进一步提出一种高效的增量查询策略,能够最大限度地利用已有查询结果减少当前查询的计算量.最后,在滴滴成都网约车数据集以及两个模拟数据集上进行大量实验,充分验证了算法的性能.     

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.     

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.     

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.     

Analysis and evaluation of V*-kNN: an efficient algorithm for moving kNN queries

The moving k nearest neighbor (MkNN) query continuously finds the k nearest neighbors of a moving query point. MkNN queries can be efficiently processed through the use of safe regions. In general, a safe region is a region within which the query point can move without changing the query answer. This paper presents an incremental safe-region-based technique for answering MkNN queries, called the V*-Diagram, as well as analysis and evaluation of its associated algorithm, V*-kNN. Traditional safe-region approaches compute a safe region based on the data objects but independent of the query location. Our approach exploits the knowledge of the query location and the boundary of the search space in addition to the data objects. As a result, V*-kNN has much smaller I/O and computation costs than existing methods. We further provide cost models to estimate the number of data accesses for V*-kNN and a competitive technique, RIS-kNN. The V*-Diagram and V*-kNN are also applicable to the domain of spatial networks and we present algorithms to construct a spatial-network V*-Diagram. Our experimental results show that V*-kNN significantly outperforms the competitive technique. The results also verify the accuracy of the cost models.     

Multiple <Emphasis Type="Italic">k</Emphasis> nearest neighbor search

The problem of kNN (k Nearest Neighbor) queries has received considerable attention in the database and information retrieval communities. Given a dataset D and a kNN query q, the k nearest neighbor algorithm finds the closest k data points to q. The applications of kNN queries are board, not only in spatio-temporal databases but also in many areas. For example, they can be used in multimedia databases, data mining, scientific databases and video retrieval. The past studies of kNN query processing did not consider the case that the server may receive multiple kNN queries at one time. Their algorithms process queries independently. Thus, the server will be busy with continuously reaccessing the database to obtain the data that have already been acquired. This results in wasting I/O costs and degrading the performance of the whole system. In this paper, we focus on this problem and propose an algorithm named COrrelated kNN query Evaluation (COKE). The main idea of COKE is an “information sharing” strategy whereby the server reuses the query results of previously executed queries for efficiently processing subsequent queries. We conduct a comprehensive set of experiments to analyze the performance of COKE and compare it with the Best-First Search (BFS) algorithm. Empirical studies indicate that COKE outperforms BFS, and achieves lower I/O costs and less running time.     

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.     

Multidimensional reverse <Emphasis Type="Italic">k</Emphasis>NN search

Given a multidimensional point q, a reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k nearest neighbors. Existing methods for processing such queries have at least one of the following deficiencies: they (i) do not support arbitrary values of k, (ii) cannot deal efficiently with database updates, (iii) are applicable only to 2D data but not to higher dimensionality, and (iv) retrieve only approximate results. Motivated by these shortcomings, we develop algorithms for exact RkNN processing with arbitrary values of k on dynamic, multidimensional datasets. Our methods utilize a conventional data-partitioning index on the dataset and do not require any pre-computation. As a second step, we extend the proposed techniques to continuous RkNN search, which returns the RkNN results for every point on a line segment. We evaluate the effectiveness of our algorithms with extensive experiments using both real and synthetic datasets.     

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.     

Scalable processing of continuous K-nearest neighbor queries with uncertain velocity

Continuous K-nearest neighbor (CKNN) query is an important type of spatio-temporal queries. Given a time interval [t_s, t_e] and a moving query object q, a CKNN query is to find the K-nearest neighbors (KNNs) of q at each time instant within [t_s, t_e]. In this paper, we focus on the issue of scalable processing of CKNN queries over moving objects with uncertain velocity. Due to the large amount of CKNN queries that need to be evaluated concurrently, efficiently processing such queries inevitably becomes more complicated. We propose an index structure, namely the CI-tree, to predetermine and organize the candidates for each query issued by the user from anywhere and anytime. When the CKNN queries are evaluated, their corresponding candidates can be rapidly retrieved by traversing the CI-tree so that the processing time is greatly reduced. A comprehensive set of experiments is performed to demonstrate the effectiveness and the efficiency of the CI-tree.     

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.     

VGQ-Vor: extending virtual grid quadtree with Voronoi diagram for mobile k nearest neighbor queries over mobile objects

Performing mobile k nearest neighbor (MkNN) queries whilst also being mobile is a challenging problem. All the mobile objects issuing queries and/or being queried aremobile. The performance of this kind of query relies heavily on the maintenance of the current locations of the objects. The index used for mobile objects must support efficient update operations and efficient query handling. This study aims to improve the performance of the MkNN queries while reducing update costs. Our approach is based on an observation that the frequency of one region changing between being occupied or not by mobile objects is much lower than the frequency of the position changes reported by the mobile objects. We first propose an virtual grid quadtree with Voronoi diagram(VGQ-Vor), which is a two-layer index structure that indexes regions occupied by mobile objects in a quadtree and builds a Voronoi diagram of the regions. Then we propose a moving k nearest neighbor (kNN) query algorithm on the VGQ-Vor and prove the correctness of the algorithm. The experimental results show that the VGQ-Vor outperforms the existing techniques (Bx-tree, Bdual-tree) by one to three orders of magnitude in most cases.