Fully dynamic distributed search trees can be balanced in O(lg2N) time

In this paper we consider the dictionary problem in a message-passing distributed environment. We introduce a new version, based on AVL-trees, of distributed search trees, the first to be fully scalable, that is, able to both grow and shrink as long as keys are inserted and deleted. We prove that in the worst case a key can be inserted, searched, or deleted with $\text{O(}\text{lg}{}^2\text{N)}$ messages. We show that for the introduced distributed search tree this bound is tight. Since the defined structure maintains the relative order of the keys, it can also support queries that refer to the linear order of keys, such as nearest neighbor or range queries.     

Fast and versatile algorithm for nearest neighbor search based on a lower bound tree

In this paper, we present a fast and versatile algorithm which can rapidly perform a variety of nearest neighbor searches. Efficiency improvement is achieved by utilizing the distance lower bound to avoid the calculation of the distance itself if the lower bound is already larger than the global minimum distance. At the preprocessing stage, the proposed algorithm constructs a lower bound tree (LB-tree) by agglomeratively clustering all the sample points to be searched. Given a query point, the lower bound of its distance to each sample point can be calculated by using the internal node of the LB-tree. To reduce the amount of lower bounds actually calculated, the winner-update search strategy is used for traversing the tree. For further efficiency improvement, data transformation can be applied to the sample and the query points. In addition to finding the nearest neighbor, the proposed algorithm can also (i) provide the k-nearest neighbors progressively; (ii) find the nearest neighbors within a specified distance threshold; and (iii) identify neighbors whose distances to the query are sufficiently close to the minimum distance of the nearest neighbor. Our experiments have shown that the proposed algorithm can save substantial computation, particularly when the distance of the query point to its nearest neighbor is relatively small compared with its distance to most other samples (which is the case for many object recognition problems).     

基于Voronoi-R*的隐私保护路网k近邻查询方法

针对已有的保护位置隐私路网k近邻查询依赖可信匿名服务器造成的安全隐患,以及服务器端全局路网索引利用效率低的缺陷,提出基于路网局部索引机制的保护位置隐私路网近邻查询方法.查询客户端通过与LBS服务器的一轮通信获取局部路网信息,生成查询位置所在路段满足l-路段多样性的匿名查询序列,并将匿名查询序列提交LBS服务器,从而避免保护位置隐私查询对可信第三方服务器的依赖.在LBS服务器端,提出基于路网基本单元划分的分段式近邻查询处理策略,对频繁查询请求路网基本单元,构建基于路网泰森多边形和R^*树的局部Vor-R^*索引结构,实现基于索引的快速查找.对非频繁请求路网基本单元,采用常规路网扩张查询处理.有效降低索引存储规模和基于全局索引进行无差异近邻查询的访问代价,在保证查询结果正确的同时,提高了LBS服务器端k近邻查询处理效率.理论分析和实验结果表明,所提方法在兼顾查询准确性的同时,有效地提高了查询处理效率.     

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.     

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.     

基于Voronoi图的组最近邻查询

组最近邻查询由于涉及多个查询点,因此比传统的最近邻查询更为复杂.充分考虑查询点的分布特征以及它们构成的几何图形的性质和特点,给出组最近邻所应满足的条件及判断组最近邻的理论方法.提出基于Voronoi图的组最近邻查询的VGNN算法,可以精确求解查询点集的最近邻.对于查询点不共线的情况,该算法的查询方式是以一点为中心、向外扩张式的;对于查询点共线的情况,该算法给出搜索范围,限定了参与计算的数据点的个数.给出基于Voronoi图的VTree索引.实验结果表明,基于VTree索引的VGNN算法具有较好的性能,并且当查询点不共线时,其性能具有较高的稳定性.     

空间数据库中的组障碍最近邻查询研究

已有的关于组最近邻查询的研究都是基于欧氏距离的,无法解决存在障碍情况下基于障碍距离的组最近邻查询问题.为此,提出障碍物环境中组最近邻查询的一种新的变体,即组障碍最近邻(group obstacle nearest neighbor, GONN)查询.GONN返回数据集中与查询点集中所有点的障碍距离之和最小的点.根据数据集中的点与查询点集的最小外包距离(minimum bounding rectangle, MBR)之间的不同位置关系,构造各种情况下查询点集的MBR相对于数据集中点的剪枝区域.利用剪枝区域剪去障碍集中对障碍距离计算无影响的障碍,给出数据集中点与查询点集之间障碍距离的计算算法.定义组障碍最近邻查询的剪枝规则,根据障碍距离计算给出组障碍最近邻查询的算法.并给出相关定理和证明.实验结果证明算法具有较高效率.     

基于不确定性平面线段的近邻查询

提出带有不确定性区域的平面线段的近邻查询问题,并根据线段之间的空间位置关系情况,对最近邻距离实现了有效的计算。主要工作有两方面：一是将平面线段的模糊区域表示成不确定性的边界区域,把线性对象影响范围的不确定性考虑进来,再根据线段位置关系的不同分别进行距离计算;二是在进行近邻查询时采用了概率方法计算出影响度,用来定量度量线段受到的影响程度。最后通过实验证明所提出的带有不确定性区域的线段近邻查询研究方法的有效性。     

基于平面线段的反向最近邻查询

反向最近邻查询是空间数据库空间查询的研究热点。目前反向最近邻查询的查询粒度都是基于一维的点．在一些空间物体不能抽象为点的情况下将其抽象为点进行反向最近邻查询,查询结果不能达到一定的精度。该文在分析基于平面线段的最近邻查询和R树结构的基础上提出了一种改进的R树－Rcd树,并给出了基于Rcd树的平面线段反向最近邻查询算法．该方法能实现平面线段的反向最近邻查询。     

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.     

基于平面线段的反向最近邻查询

反向最近邻查询是空间数据库空间查询的研究热点。目前反向最近邻查询的查询粒度都是基于一维的点,在一些空间物体不能抽象为点的情况下将其抽象为点进行反向最近邻查询,查询结果不能达到一定的精度。该文在分析基于平面线段的最近邻查询和R树结构的基础上提出了一种改进的R树—Rcd树,并给出了基于Rcd树的平面线段反向最近邻查询算法,该方法能实现平面线段的反向最近邻查询。     

局部范围受限的多类型最近邻查询

多类型最近邻查询在现实中的应用范围比传统的最近邻查询广泛.基于多类型最近邻查询,提出局部范围受限的多类型最近邻查询(PCMTNN)概念,针对范围约束是任意简单多边形区域的数据集给出PCMTNN算法,利用椭圆最小外切矩形的易求性和与椭圆本身覆盖区域的最近似性特点缩小了搜索范围,并用一个链表结构实现了在一次R树的遍历过程中找到包含在所有搜索区域内的数据集中点的过程,从而大幅度减少了无用点的访问数量.实验结果分析表明算法具有较好的性能.     

On multi-type reverse nearest neighbor search

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

基于新型索引结构的反最近邻查询

为了提高反最近邻问题的查询效率,首先给出了空间数据的最小包围正方形定义和空间数据矩形的4种序的定义.依据这些定义,提出了一种新的空间数据索引结构——基于最小包围正方形和最近邻距离的索引树(index tree based on the minimum bounding square and the distance of nearest neighbor, MBDNN-tree),该索引结构运用了R-树中分割空间数据的思想,将数据点用其基于最近邻距离的最小包围正方形表示,记为MBSD(minimum bounding square based on nearest neighbor distance),利用多种序关系对原始点集进行划分,从上至下、从左至右地按照结点几何分布以及对应的序关系构造树的各层结点.对建立MBDNN-树所需要的预处理过程以及构造过程的算法进行了详细描述和证明分析,给出了MBDNN-树的性质.在此基础上,给出了MBDNN-树进行反最近邻查询的剪枝规则,进而给出了MBDNN-树进行反最近邻查询的算法及其算法分析.反最近邻查询算法利用了MBDNN-树中同层结点之间的几何有序性,有效地减少了结点的访问数量,从而提高了查询效率.最后对基于此结构的反最近邻查询算法进行实验分析.实验表明：基于MBDNN-树的反最近邻查询算法的查询性能有较大的提高.     

球面上的最近邻查询方法研究

球面上的最近邻查询在空间数据库最近邻查询领域具有重要的意义。为了处理球面上的最近邻查询问题,针对球面上数据对象点的特征和近邻查询的需要,给出了处理球面上最近邻查询的3种方法：利用球面voronoi图计算最近邻方法（VNS）;利用欧氏空间内的空间数据索引结构方法（SPINS）和降维方法（APNS）。进一步,在动态的密集数据集和动态的稀松数据集两种典型的组合情况下分别着重对3 种方法处理最近邻查询的性能进行了实验比较。理论分析和实验结果表明,给出的3种方法可较好地处理球面上具有不同性质特征的空间数据对象点的近邻查询问题。     

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.     

基于Voronoi图及其对偶图的反最近邻查询

最近邻查询是地理信息系统领域经常遇到的问题,而反最近邻查询是在最近邻查询的基础上提出的一种新的查询类型。在分析利用Voronoi图进行最近邻查询的基础上,提出了基于Voronoi图及其对偶图Delaunay图的反最近邻查询,大大缩小了在海量空间数据库中进行反最近邻查询的查询范围。     

时间依赖路网中反向k近邻查询

在现存的反向k近邻查询方案中,比较高效的研究大多集中在欧氏空间或者静态路网,对时间依赖路网中的反向k近邻查询的研究相对较少。已有算法在兴趣点密度稀疏或者k值较大时,查询效率较低。对此,提出了基于子网划分的反向k近邻查询算法mTD-SubG。首先,将整个路网划分为大小相同的子网,通过子网的边界节点向其他子网进行扩展,加快对路网中兴趣点的查找速度;其次,利用剪枝技术缩小路网的扩展范围;最后, 利用已有时间依赖路网下的近邻查询算法,判定查找到的兴趣点是否为反向k近邻结果。实验中将mTD-SubG算法与已有算法mTD-Eager进行对比,结果表明mTD-SubG算法的响应时间比mTD-Eager算法减少了85.05%,遍历节点个数比mTD-Eager算法减少了51.40%。     

基于查询集空间分布的聚合最近邻查询算法

聚合最近邻查询涉及到多个查询对象,因此比传统最近邻查询更复杂,而且其查询集空间分布特征暗含了查询集聚合最近邻的区域分布信息。充分考虑查询集分布特征,给出了利用分布特征指导聚合最近邻搜索的方法,并以此提出了一种新的聚合最近邻查询算法——AM算法。AM算法能动态地捕捉并利用查询集空间分布特征,使得对数据点的搜索按正确的次序进行,避免对不必要数据点的搜索。最后通过实验验证了AM算法的高效性。