Voronoi-based range and continuous range query processing in mobile databases

With the wide availability of mobile devices (smart phones, iPhones, etc.), mobile location-based queries are increasingly in demand. One of the most frequent queries is range search which returns objects of interest within a pre-defined area. Most of the existing methods are based on the road network expansion method – expanding all nodes (intersections and objects) and computing the distance of each node to the query point. Since road networks are extremely complex, node expansion approaches are inefficient. In this paper, we propose a method, Voronoi Range Search (VRS) based on the Voronoi diagram, to process range search queries efficiently and accurately by partitioning the road networks to some special polygons. Then we further propose Voronoi Continuous Range (VCR) to satisfy the requirement for continuous range search queries (moving queries) based on VRS. Our empirical experiments show that VRS and VCR surpass all their rivals for both static and moving queries.     

Effectiveness of NAQ-tree in handling reverse nearest-neighbor queries in high-dimensional metric space

Reverse nearest-neighbor (RNN) query processing is important for many applications such as decision-support systems, profile-based marketing and molecular biology; consequently, RNN query processing has attracted considerable attention in the research community in recent years. Most existing approaches for RNN query processing either rely on nearest-neighbor pre-computation or work for specific data space (e.g., the Euclidean space). The only method for RNN query processing in metric space is based on the M-tree. In this paper, we propose an approach for RNN query processing in high-dimensional metric space using distance-based index structure (in particular, NAQ-tree that outperforms the other distance-based index structures as we have already verified in a previous study). In high-dimensional space, the properties of distance-based index structure provide strong pruning rules than the M-tree. In addition, unlike the previous work, our approach integrates the filtering and verification steps and uses the information obtained in the verification stage to further improve the filtering rate. Our approach delivers results incrementally and hence well serves real-time applications. The reported experimental results demonstrate the applicability and effectiveness of the proposed NAQ-tree-based RNN approach.     

Voronoi-based multi-level range search in mobile navigation

Due to the universality and importance of range search queries processing in mobile and spatial databases as well as in geographic information system (GIS), numerous approaches on range search algorithms have been proposed in recent years. But ordinary range search queries focus only on a specific type of point objects. For queries which require to retrieve objects of interest locating in a particular region, ordinary range search could not get the expected results. In addition, most existing range search methods need to perform a searching on each road segments within the pre-defined range, which decreases the performance of range search. In this paper, we design a weighted network Voronoi diagram and propose a high-performance multilevel range search query processing that retrieves a set of objects locating in some specified region within the searching range. The experimental results show that our proposed algorithm runs very efficiently and outperforms its main competitor.     

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。     

k-Nearest Neighbor Query Processing Algorithms for a Query Region in Road Networks

Recent development of wireless communication technologies and the popularity of smart phones are making location-based services (LBS) popular. However, requesting queries to LBS servers with users’ exact locations may threat the privacy of users. Therefore, there have been many researches on generating a cloaked query region for user privacy protection. Consequently, an effcient query processing algorithm for a query region is required. So, in this paper, we propose k-nearest neighbor query (k-NN) processing algorithms for a query region in road networks. To effciently retrieve k-NN points of interest (POIs), we make use of the Island index. We also propose a method that generates an adaptive Island index to improve the query processing performance and storage usage. Finally, we show by our performance analysis that our k-NN query processing algorithms outperform the existing k-Range Nearest Neighbor (kRNN) algorithm in terms of network expansion cost and query processing time.     

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.     

XMin: Minimizing Tree Pattern Queries with Minimality Guarantee

Due to wide use of XPath, the problem of efficiently processing XPath queries has recently received a lot of attention. In particular, a considerable effort has been devoted to minimizing XPath queries since the efficiency of query processing greatly depends on the size of the query. Research work in this area can be classified into two categories: constraint-independent minimization and constraint-dependent minimization. The former minimizes queries in the absence of integrity constraints while the latter in the presence of them. For a linear path query, which is an XPath query without branching predicates, existing constraint-independent minimization methods are generally known to be unable to minimize the query without processing the query itself. Most recently, however, by using the DataGuide, a representative structural summary of XML data, a constraint-independent method that minimizes linear path queries in a top-down fashion has been proposed. Nevertheless, this method can fail to find a minimal query since it minimizes a query by merely erasing labels from the original query whereas a minimal query could include labels that are not present in the original query. In this paper, we propose a bottom-up approach called XMin that guarantees finding a minimal query for a given tree pattern query by using the DataGuide without processing the query itself. For the linear path query, we first show that the sequence of labels occurring in the minimal query is a subsequence of every schema label sequence that matches the original query. Here, the schema label sequence for a node is the sequence of labels from the root of XML data to the node. We then propose iterative subsequence generation that iteratively generates subsequences from the shortest schema label sequence matching the original query in a bottom-up fashion and tests query equivalence. Using iterative subsequence generation, we can always find a minimal query and we formally prove this guarantee. We also propose an extended algorithm that guarantees the minimality for the tree pattern query, which is a linear path query with branching predicates. These methods have been prototyped in a full-fledged object-relational DBMS. The experimental results using real and synthetic data sets show the practicality of our method.     

Query-aware location anonymization for road networks

Recently, several techniques have been proposed to protect the user location privacy for location-based services in the Euclidean space. Applying these techniques directly to the road network environment would lead to privacy leakage and inefficient query processing. In this paper, we propose a new location anonymization algorithm that is designed specifically for the road network environment. Our algorithm relies on the commonly used concept of spatial cloaking, where a user location is cloaked into a set of connected road segments of a minimum total length L{\cal L} including at least K{\cal K} users. Our algorithm is “query-aware” as it takes into account the query execution cost at a database server and the query quality, i.e., the number of objects returned to users by the database server, during the location anonymization process. In particular, we develop a new cost function that balances between the query execution cost and the query quality. Then, we introduce two versions of our algorithm, namely, pure greedy and randomized greedy, that aim to minimize the developed cost function and satisfy the user specified privacy requirements. To accommodate intervals with a high workload, we introduce a shared execution paradigm that boosts the scalability of our location anonymization algorithm and the database server to support large numbers of queries received in a short time period. Extensive experimental results show that our algorithms are more efficient and scalable than the state-of-the-art technique, in terms of both query execution cost and query quality. The results also show that our algorithms have very strong resilience to two privacy attacks, namely, the replay attack and the center-of-cloaked-area attack.     

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.     

路网中基于Voronoi图的反向最近邻查询方法

针对已有的在路网中的反向最近邻(Reverse Nearest Neighbor,RNN)查询方法存在的不足,提出了利用网络Voronoi图(Network Voronoi Diagram,NVD)的NVD-RNN算法,该算法具有较好的效果,它把路网划分成小的Voronoi区域,并且采用了两个过程:过滤过程和精炼过程。过滤过程主要是提前存储可能的查询结果。精炼过程主要是从可能的结果集合中找到查询结果。并且进一步给出了处理新增加点的ADDNVD-RNN算法和处理删除点的DENVD-RNN算法。实验表明,该算法在处理路网中的反向最近邻问题时有明显的优势。     

基于Voronoi图的反向最近邻查询

为了解决反向最近邻查询问题,利用Voronoi图及数据集中点的凸包进行反向最近邻查询,通过判断查询点与凸包的位置关系,可去除大量的数据点,并且给出在数据点被加入或删除后,对查询点的反向最近邻变化情况的判断方法与算法。为了便于查询,设计相应的空间存储数据结构。比较分析表明,该方法在处理多个查询点的反向最近邻时有一定的优势。     

Restricting Voronoi diagrams to meshes using corner validation

Restricted Voronoi diagrams are a fundamental geometric structure used in many applications such as surface reconstruction from point sets or optimal transport. Given a set of sites V = { v _k}ⁿ_k=1 ? ?^d and a mesh X with vertices in ?^d connected by triangles, the restricted Voronoi diagram partitions X by computing for each site the portion of X for which the site is the nearest. The restricted Voronoi diagram is the intersection between the regular Voronoi diagram and the mesh. Depending on the site distribution or the ambient space dimension computing the regular Voronoi diagram may not be feasible using classical algorithms. In this paper, we extend Lévy and Bonneel's approach [ LB12 ] based on nearest neighbor queries. We show that their method is limited when the sites are not located on X . We propose a new algorithm for computing restricted Voronoi which reduces the number of sites considered for each triangle of the mesh and scales smoothly when the sites are far from the surface.     

空间数据库中的线段k近邻查询研究

K近邻查询是空间数据库中的重要查询之一,k近邻查询在内容的相似性检索、模式识别、地理信息系统中有重要应用。针对现有k近邻查询都是基于点查询的情况,提出基于平面线段的k近邻查询,查找线段集中给定查询点的k个最近线段。给出基于Voronoi图的线段k近邻查询算法及给出相关定理和证明。该算法通过线段Voronoi图的邻接特性找到一个候选集,然后从中找到最终结果。通过随机数据的实验证明,所提算法明显优于线性扫描算法和基于R树的k近邻查询算法。     

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.     

空间数据库中一种自适应的缓存替换策略

随着近年来空间数据库研究和应用的不断深入,针对空间数据库中数据组织和查询的特征来设计缓存页面替换策略成为一个新的研究问题.Voronoi图是一种重要的空间数据库组织技术,在处理kNN查询时具有非常好的性能.针对Voronoi图组织的空间数据库,首先利用空间局部性提出了一种基于欧氏距离的替换策略,在发生页面失效时选择距离上一次访问页面欧氏距离最远的页面进行替换;进一步,针对不同kNN查询的搜索空间大小差异非常大的特点,在LIRS替换策略基础上提出一种自适应替换策略,通过对HIR页面占缓存比例自动调整来适应不同的查询.综合两者,形成基于欧氏距离的自适应缓存页面替换算法AELIRS.大量实验表明,在缓存大小与搜索空间大范围变动中,AELIRS始终优于其他替换策略.     

Grid-partition index: a hybrid method for nearest-neighbor queries in wireless location-based services

Traditional nearest-neighbor (NN) search is based on two basic indexing approaches: object-based indexing and solution-based indexing. The former is constructed based on the locations of data objects: using some distance heuristics on object locations. The latter is built on a precomputed solution space. Thus, NN queries can be reduced to and processed as simple point queries in this solution space. Both approaches exhibit some disadvantages, especially when employed for wireless data broadcast in mobile computing environments. In this paper, we introduce a new index method, called the grid-partition index, to support NN search in both on-demand access and periodic broadcast modes of mobile computing. The grid-partition index is constructed based on the Voronoi diagram, i.e., the solution space of NN queries. However, it has two distinctive characteristics. First, it divides the solution space into grid cells such that a query point can be efficiently mapped into a grid cell around which the nearest object is located. This significantly reduces the search space. Second, the grid-partition index stores the objects that are potential NNs of any query falling within the cell. The storage of objects, instead of the Voronoi cells, makes the grid-partition index a hybrid of the solution-based and object-based approaches. As a result, it achieves a much more compact representation than the pure solution-based approach and avoids backtracked traversals required in the typical object-based approach, thus realizing the advantages of both approaches. We develop an incremental construction algorithm to address the issue of object update. In addition, we present a cost model to approximate the search cost of different grid partitioning schemes. The performances of the grid-partition index and existing indexes are evaluated using both synthetic and real data. The results show that, overall, the grid-partition index significantly outperforms object-based indexes and solution-based indexes. Furthermore, we extend the grid-partition index to support continuous-nearest-neighbor search. Both algorithms and experimental results are presented. Edited by R. Guting     

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.     

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.     

基于Voronoi图的连续反向最近邻查询

为解决动态环境中移动点的连续反向最近邻查询问题,将连续反向最近邻查询分为单色和双色2种情况进行研究。利用移动点Voronoi图,分别给出单色连续反向最近邻查询算法、双色连续反向最近邻查询算法以及相关定理,对算法正确性和可终止性进行证明,分析算法时间复杂性。按照移动点Voronoi图的拓扑结构是否改变分为2种情况,分析每种情况下候选所在区域的变化,在变化区域内进行Voronoi图的重构,得到对应的解决方法。在多数情况下,该算法只需生成局部移动点的Voronoi图即可找到结果,减小了连续反向最近邻查询的代价。     

Progressive evaluation of nested aggregate queries

In many decision-making scenarios, decision makers require rapid feedback to their queries, which typically involve aggregates. The traditional blocking execution model can no longer meet the demands of these users. One promising approach in the literature, called online aggregation, evaluates an aggregation query progressively as follows: as soon as certain data have been evaluated, approximate answers are produced with their respective running confidence intervals; as more data are examined, the answers and their corresponding running confidence intervals are refined. In this paper, we extend this approach to handle nested queries with aggregates (i.e., at least one inner query block is an aggregate query) by providing users with (approximate) answers progressively as the inner aggregation query blocks are evaluated. We address the new issues pose by nested queries. In particular, the answer space begins with a superset of the final answers and is refined as the aggregates from the inner query blocks are refined. For the intermediary answers to be meaningful, they have to be interpreted with the aggregates from the inner queries. We also propose a multi-threaded model in evaluating such queries: each query block is assigned to a thread, and the threads can be evaluated concurrently and independently. The time slice across the threads is nondeterministic in the sense that the user controls the relative rate at which these subqueries are being evaluated. For enumerative nested queries, we propose a priority-based evaluation strategy to present answers that are certainly in the final answer space first, before presenting those whose validity may be affected as the inner query aggregates are refined. We implemented a prototype system using Java and evaluated our system. Results for nested queries with a level and multiple levels of nesting are reported. Our results show the effectiveness of the proposed mechanisms in providing progressive feedback that reduces the initial waiting time of users significantly without sacrificing the quality of the answers. Received April 25, 2000 / Accepted June 27, 2000