An efficient animation of wrinkled cloth with approximate implicit integration

This paper presents an efficient method for creating the animation of flexible objects. The mass-spring model was used to represent flexible objects. The easiest approach to creating animation with the mass-spring model is the explicit Euler method, but the method has a serious weakness in that it suffers from an instability problem. The implicit integration method is a possible solution, but a critical flaw of the implicit method is that it involves a large linear system. This paper presents an approximate implicit method for the mass-spring model. The proposed technique updates with stability the state of n mass points in O(n) time when the number of total springs is O(n). In order to increase the efficiency of simulation or reduce the numerical errors of the proposed approximate implicit method, the number of mass points must be as small as possible. However, coarse discretization with a small number of mass points generates an unrealistic appearance for a cloth model. By introducing a wrinkled cubic spline curve, we propose a new technique that generates realistic details of the cloth model, even though a small number of mass points are used for simulation.     

Searching in metric spaces by spatial approximation

We propose a new data structure to search in metric spaces. A metric space is formed by a collection of objects and a distance function defined among them which satisfies the triangle inequality. The goal is, given a set of objects and a query, retrieve those objects close enough to the query. The complexity measure is the number of distances computed to achieve this goal. Our data structure, called sa-tree (“spatial approximation tree”), is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures. We analyze our method and show that the number of distance evaluations to search among n objects is sublinear. We show experimentally that the sa-tree is the best existing technique when the metric space is hard to search or the query has low selectivity. These are the most important unsolved cases in real applications. As a practical advantage, our data structure is one of the few that does not need to tune parameters, which makes it appealing for use by non-experts. Edited by R. Sacks-Davis Received: 17 April 2001 / Accepted: 24 January 2002 / Published online: 14 May 2002     

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.     

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.     

大规模散乱点的k邻域快速搜索算法

针对大规模散乱点数据k最近邻域搜索速度慢和稳定性差的问题,提出一种新的k邻域快速搜索算法.首先,引入空间分块策略将数据集中的点归入不同的子空间;其次,动态控制搜索步长的改变量,根据点到其自身小立方体边界的最小距离保证搜索结果的准确性;最后,通过改变预筛选点数量的右侧控制阈值来消除已有算法中由于初始数值不当引起的死循环.实验结果表明该算法对初始搜索步长、搜索步长增量、采样密度和不同的拓扑结构具有较强的稳定性,并且能更快地完成k邻域搜索.     

Shape similarity by homotopic deformation

nk +n log n) time, where n is the number of vertices in the polygonal shapes and k is an index to indicate how the target shape is convoluted. Experimental results show the feasibility of our approach. Extending the method for comparison of scenes with mutiple objects is also discussed.     

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.     

Application of density-based outlier detection to database activity monitoring

To prevent internal data leakage, database activity monitoring uses software agents to analyze protocol traffic over networks and to observe local database activities. However, the large size of data obtained from database activity monitoring has presented a significant barrier to effective monitoring and analysis of database activities. In this paper, we present database activity monitoring by means of a density-based outlier detection method and a commercial database activity monitoring solution. In order to provide efficient computing of outlier detection, we exploited a kd-tree index and an Approximated k-nearest neighbors (ANN) search method. By these means, the outlier computation time could be significantly reduced. The proposed methodology was successfully applied to a very large log dataset collected from the Korea Atomic Energy Research Institute (KAERI). The results showed that the proposed method can effectively detect outliers of database activities in a shorter computation time.     

Accelerated k-nearest neighbors algorithm based on principal component analysis for text categorization

Text categorization is a significant technique to manage the surging text data on the Internet.The k-nearest neighbors(kNN) algorithm is an effective,but not efficient,classification model for text categorization.In this paper,we propose an effective strategy to accelerate the standard kNN,based on a simple principle:usually,near points in space are also near when they are projected into a direction,which means that distant points in the projection direction are also distant in the original space.Using the proposed strategy,most of the irrelevant points can be removed when searching for the k-nearest neighbors of a query point,which greatly decreases the computation cost.Experimental results show that the proposed strategy greatly improves the time performance of the standard kNN,with little degradation in accuracy.Specifically,it is superior in applications that have large and high-dimensional datasets.     

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.

     

Probably correct k-nearest neighbor search in high dimensions

A novel approach for k-nearest neighbor (k-NN) searching with Euclidean metric is described. It is well known that many sophisticated algorithms cannot beat the brute-force algorithm when the dimensionality is high. In this study, a probably correct approach, in which the correct set of k-nearest neighbors is obtained in high probability, is proposed for greatly reducing the searching time. We exploit the marginal distribution of the k th nearest neighbors in low dimensions, which is estimated from the stored data (an empirical percentile approach). We analyze the basic nature of the marginal distribution and show the advantage of the implemented algorithm, which is a probabilistic variant of the partial distance searching. Its query time is sublinear in data size n, that is, O(mnδ) with δ=o(1) in n and δ≤1, for any fixed dimension m.     

Effective protocols for kNN search on broadcast multi-dimensional index trees

In a wireless mobile environment, data broadcasting provides an efficient way to disseminate data. Via data broadcasting, a server can provide location-based services to a large client population in a wireless environment. Among different location-based services, the k nearest neighbors (kNN) search is important and is used to find the k closest objects to a given point. However, the kNN search in a broadcast environment is particularly challenging due to the sequential access to the data on a broadcast channel. We propose efficient protocols for the kNN search on a broadcast R-tree, which is a popular multi-dimensional index tree, in a wireless broadcast environment in terms of latency and tuning time as well as memory usage. We investigate how a server schedules the broadcast and provide the corresponding kNN search algorithms at the mobile clients. One of our kNN search protocols further allows a kNN search to start at an arbitrary time instance and it can skip the waiting time for the beginning of a broadcast cycle, thereby reducing the latency. The experimental results validate that our mechanisms achieve the objectives.     

Dense Neighborhoods on Affinity Graph

In this paper, we study the problem of how to reliably compute neighborhoods on affinity graphs. The k-nearest neighbors (kNN) is one of the most fundamental and simple methods widely used in many tasks, such as classification and graph construction. Previous research focused on how to efficiently compute kNN on vectorial data. However, most real-world data have no vectorial representations, and only have affinity graphs which may contain unreliable affinities. Since the kNN of an object o is a set of k objects with the highest affinities to o, it is easily disturbed by errors in pairwise affinities between o and other objects, and also it cannot well preserve the structure underlying the data. To reliably analyze the neighborhood on affinity graphs, we define the k-dense neighborhood (kDN), which considers all pairwise affinities within the neighborhood, i.e., not only the affinities between o and its neighbors but also between the neighbors. For an object o, its kDN is a set kDN(o) of k objects which maximizes the sum of all pairwise affinities of objects in the set {o}∪kDN(o). We analyze the properties of kDN, and propose an efficient algorithm to compute it. Both theoretic analysis and experimental results on shape retrieval, semi-supervised learning, point set matching and data clustering show that kDN significantly outperforms kNN on affinity graphs, especially when many pairwise affinities are unreliable.     

The hB^\Pi-tree: a multi-attribute index supporting concurrency, recovery and node consolidation

We propose a new multi-attribute index. Our approach combines the hB-tree, a multi-attribute index, and the -tree, an abstract index which offers efficient concurrency and recovery methods. We call the resulting method the hB-tree. We describe several versions of the hB-tree, each using a different node-splitting and index-term-posting algorithm. We also describe a new node deletion algorithm. We have implemented all the versions of the hB-tree. Our performance results show that even the version that offers no performance guarantees, actually performs very well in terms of storage utilization, index size (fan-out), exact-match and range searching, under various data types and distributions. We have also shown that our index is fairly insensitive to increases in dimension. Thus, it is suitable for indexing high-dimensional applications. This property and the fact that all our versions of the hB-tree can use the -tree concurrency and recovery algorithms make the hB-tree a promising candidate for inclusion in a general-purpose DBMS. Edited by R. Sacks-Davis. Received 27 June 1994 / Accepted 26 September 1995     

The BG distributed simulation algorithm

We present a shared memory algorithm that allows a set of f+1 processes to wait-free “simulate” a larger system of n processes, that may also exhibit up to f stopping failures. Applying this simulation algorithm to the k-set-agreement problem enables conversion of an arbitrary k-fault-tolerant{\it n}-process solution for the k-set-agreement problem into a wait-free k+1-process solution for the same problem. Since the k+1-processk-set-agreement problem has been shown to have no wait-free solution [5,18,26], this transformation implies that there is no k-fault-tolerant solution to the n-process k-set-agreement problem, for any n. More generally, the algorithm satisfies the requirements of a fault-tolerant distributed simulation.\/ The distributed simulation implements a notion of fault-tolerant reducibility\/ between decision problems. This paper defines these notions and gives examples of their application to fundamental distributed computing problems. The algorithm is presented and verified in terms of I/O automata. The presentation has a great deal of interesting modularity, expressed by I/O automaton composition and both forward and backward simulation relations. Composition is used to include a safe agreement\/ module as a subroutine. Forward and backward simulation relations are used to view the algorithm as implementing a multi-try snapshot\/ strategy. The main algorithm works in snapshot shared memory systems; a simple modification of the algorithm that works in read/write shared memory systems is also presented. Received: February 2001 / Accepted: February 2001     

Chromatic distribution of k-nearest neighbors of a line segment in a planar colored point set

Let P be a set of n colored points distributed arbitrarily in R². The chromatic distribution of the k-nearest neighbors of a query line segment ? is to report the number of points of each color among the k-nearest points of the query line segment. While solving this problem, we have encountered another interesting problem, namely the semicircular range counting query. Here a set of n points is given. The objective is to report the number of points inside a given semicircular range. We propose a simple algorithm for this problem with preprocessing time and space complexity O(n³), and the query time complexity O(logn). Finally, we propose the algorithm for reporting the chromatic distribution of k nearest neighbors of a query line segment. Using our proposed technique for semicircular range counting query, it runs in O(log²n) time.     

Fast string correction with Levenshtein automata

The Levenshtein distance between two words is the minimal number of insertions, deletions or substitutions that are needed to transform one word into the other. Levenshtein automata of degree n for a word W are defined as finite state automata that recognize the set of all words V where the Levenshtein distance between V and W does not exceed n. We show how to compute, for any fixed bound n and any input word W, a deterministic Levenshtein automaton of degree n for W in time linear to the length of W. Given an electronic dictionary that is implemented in the form of a trie or a finite state automaton, the Levenshtein automaton for W can be used to control search in the lexicon in such a way that exactly the lexical words V are generated where the Levenshtein distance between V and W does not exceed the given bound. This leads to a very fast method for correcting corrupted input words of unrestricted text using large electronic dictionaries. We then introduce a second method that avoids the explicit computation of Levenshtein automata and leads to even improved efficiency. Evaluation results are given that also address variants of both methods that are based on modified Levenshtein distances where further primitive edit operations (transpositions, merges and splits) are used. Received: 13 February 2002 / Accepted: 13 March 2002     

Failure detection and consensus in the crash-recovery model

Summary. We study the problems of failure detection and consensus in asynchronous systems in which processes may crash and recover, and links may lose messages. We first propose new failure detectors that are particularly suitable to the crash-recovery model. We next determine under what conditions stable storage is necessary to solve consensus in this model. Using the new failure detectors, we give two consensus algorithms that match these conditions: one requires stable storage and the other does not. Both algorithms tolerate link failures and are particularly efficient in the runs that are most likely in practice – those with no failures or failure detector mistakes. In such runs, consensus is achieved within time and with 4 n messages, where is the maximum message delay and n is the number of processes in the system. Received: May 1998 / Accepted: November 1999     

An improved branch and bound algorithm for computing k-nearest neighbors

In 1975 Fukunaga and Narendra proposed an efficient branch and bound algorithm for computing k-nearest neighbors. Their algorithm, after a hierarchical decomposition of the design set into disjoint subsets, employs two rules in order to eliminate the necessity of calculating many distances. This correspondence discusses the applicability of two additional rules for a further reduction of the number of distance computations. Experimental results using samples from bivariate Gaussian and uniform distributions suggest that the number of distance computations required by the modified is typicaly one fourth of that of the Fukunaga-Narendra algorithm.     

Efficient KNN search by linear projection of image clusters

K‐nearest neighbors (KNN) search in a high‐dimensional vector space is an important paradigm for a variety of applications. Despite the continuous efforts in the past years, algorithms to find the exact KNN answer set at high dimensions are outperformed by a linear scan method. In this paper, we propose a technique to find the exact KNN image objects to a given query object. First, the proposed technique clusters the images using a self‐organizing map algorithm and then it projects the found clusters into points in a linear space based on the distances between each cluster and a selected reference point. These projected points are then organized in a simple, compact, and yet fast index structure called array‐index. Unlike most indexes that support KNN search, the array‐index requires a storage space that is linear in the number of projected points. The experiments show that the proposed technique is more efficient and robust to dimensionality as compared to other well‐known techniques because of its simplicity and compactness. © 2011 Wiley Periodicals, Inc.