Laplacian spectrum analysis and spanning tree algorithm for circuit partitioning problems

The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.     

基于图论的频繁模式挖掘

对图数据频繁模式的挖掘是近年的研究热点．选择了惟一标号图进行分析,结合图论和频集生成的算法,提出了基于Aproiri思想、运用矩阵乘法的AMGM算法和基于SFP树的SFP算法．它们可有效地挖掘简单图中连通频繁子图．实验表明,这两个算法是十分有效的,其中SFP算法的性能优于AMGM．该算法还被运用于发现Web上的权威页面和社团,具有良好的效果．     

知识图谱划分算法研究综述

知识图谱是人工智能的重要基石,因其包含丰富的图结构和属性信息而受到广泛关注.知识图谱可以精确语义描述现实世界中的各种实体及其联系,其中顶点表示实体,边表示实体间的联系.知识图谱划分是大规模知识图谱分布式处理的首要工作,对知识图谱分布式存储、查询、推理和挖掘起基础支撑作用.随着知识图谱数据规模及分布式处理需求的不断增长,...     

Adaptive Algorithms for Join Processing in Distributed Database Systems

Distributed query processing algorithms usually perform data reduction by using a semijoin program, but the problem with these approaches is that they still require an explicit join of the reduced relations in the final phase. We introduce an efficient algorithm for join processing in distributed database systems that makes use of bipartite graphs in order to reduce data communication costs and local processing costs. The bipartite graphs represent the tuples that can be joined in two relations taking also into account the reduction state of the relations. This algorithm fully reduces the relations at each site. We then present an adaptive algorithm for response time optimization that takes into account the system configuration, i.e., the additional resources available and the data characteristics, in order to select the best strategy for response time minimization. We also report on the results of a set of experiments which show that our algorithms outperform a number of the recently proposed methods for total processing time and response time minimization.     

一种基于GN算法的动态图划分方法

随着图规模的急剧增长,对动态图进行实时处理的需求日益增加。大多现有的算法针对静态图划分是有效的,直接用其处理动态图会带来较大的通信开销。针对该问题,提出一种基于GN算法的动态图划分方法。首先收集一段时间内加入动态图中的顶点;然后,利用GN算法对这些新加入的顶点进行预划分,产生若干个内部联系紧密的社区;最后,将预划分产生的社区结果插入到已经划分好的当前图中。实验从交叉边数和负载均衡度两方面将该方法与传统流式划分方法进行比较,结果表明,在公开数据集上,该方法的交叉边数降低了13%,负载均衡度减少了42.3%。由此可见,该方法的划分质量明显优于传统的流式划分方法。     

海量医学数据处理框架及快速体绘制算法

设计并实现了一套针对海量数据的处理和分析算法框架,并将其融入实验室早先开发完成的医学影像算法研发平台MITK(medical imaging toolkit)中,真正建立起一个海量医学影像数据的处理平台,并在此基础上研究了针对海量数据的基于光线投射和三维纹理的快速体绘制算法,提出了一种半自适应分块的方法对原始数据进行分块,在不对分块速度产生太大影响的基础上得到了更好的分块结果,同时使用图形硬件来进一步加速整个算法的绘制流程.实验结果表明了该平台和算法对于海量医学数据处理和可视化的有效性.     

An objective function for vertically partitioning relations in distributed databases and its analysis

Partitioning and allocation of relations is an important component of the distributed database design. Several approaches (and algorithms) have been proposed for clustering data for pattern classification and for partitioning relations in distributed databases. Most of the approaches used for classification use square-error criterion. In contrast, most of the approaches proposed for partitioning of relations are eitherad hoc solutions or solutions for special cases (e.g., binary vertical partitioning).In this paper, we first highlight the differences between the approaches taken for pattern classification and for distributed databases. Then an objective function for vertical partitioning of relations is derived using the square-error criterion commonly used in data clustering. The objective function derived generalizes and subsumes earlier work on vertical partitioning. Furthermore, the approach proposed in this paper is shown to be useful for comparing previously developed algorithms for vertical partitioning. The objective function has also been extended to include additional information, such as transaction types, different local and remote accessing costs and replication. Finally, we discuss the implementation of a distributed database design testbed. Recommended by: A. Sheth     

基于局部有限搜索的无向图近似最大团快速求解算法

无向图最大团求解是一个著名的NP-完全问题,解决该问题的经典算法基本上都采用完全精确搜索策略。鉴于NP-完全问题本身所固有的复杂性,这些算法或许仅适用于某些特殊的小规模图,对于具有大规模顶点和边的复杂图还是显得无力,难以适用。针对完全精确搜索策略下的无向图最大团求解算法的大部分时间都用于对图进行额外而无效的查找的问题,采用分划递归技术将图划分为邻接子图和悬挂子图,然后对邻接子图进行递归求解,而对悬挂子图则通过设置搜索范围控制函数进行局部有限搜索。在DIMACS数据集上将所提算法与当前主要的最大团求解算法进行对比实验,结果表明,文中提出的局部有限搜索求解策略能在75%的基准数据上获得最大团,剩下不能得到最大团的数据实际上也可以获得接近于最大团的近似最大团,但算法的平均求解时间仅为目前最大团精确求解算法的20%左右。因此,在很多最大团非精确要求的场景中,所提算法具有极高的应用价值。     

轨迹图谱：一种基于知识图谱结构的轨迹信息抽取方法

现有的这些方法对轨迹数据需根据不同的应用设计不同的数据结构、存储结构、查询算法等,缺少通用性。为了使得轨迹数据更具有通用性,提出了将轨迹转换为知识图谱结构的方法。该方法结合轨迹数据的特点及知识图谱的定义,分别抽取出轨迹数据的实体、关系、属性并构造了轨迹图谱。转换为轨迹图谱后的轨迹数据具有通用的图结构,可直接支持轨迹的基本查询、范围查询、最近邻查询、关键词查询、模式查询等,并可轻易地将其添加到各种现有的知识库中。最终通过在真实数据集上的实验,对比了各类轨迹查询在轨迹图谱方法及普通数据库方法中的表现,证明了轨迹图谱方法的高效性及通用性。     

Converting discrete images to partitioning trees

The discrete space representation of most scientific datasets, generated through instruments or by sampling continuously defined fields, while being simple, is also verbose and structureless. We propose the use of a particular spatial structure, the binary space partitioning tree as a new representation to perform efficient geometric computation in discretely defined domains. The ease of performing affine transformations, set operations between objects, and correct implementation of transparency makes the partitioning tree a good candidate for probing and analyzing medical reconstructions, in such applications as surgery planning and prostheses design. The multiresolution characteristics of the representation can be exploited to perform such operations at interactive rates by smooth variation of the amount of geometry. Application to ultrasound data segmentation and visualization is proposed. The paper describes methods for constructing partitioning trees from a discrete image/volume data set. Discrete space operators developed for edge detection are used to locate discontinuities in the image from which lines/planes containing the discontinuities are fitted by using either the Hough transform or a hyperplane sort. A multiresolution representation can be generated by ordering the choice of hyperplanes by the magnitude of the discontinuities. Various approximations can be obtained by pruning the tree according to an error metric. The segmentation of the image into edgeless regions can yield significant data compression. A hierarchical encoding schema for both lossless and lossy encodings is described     

An enhanced bitstring encoding for exact maximum clique search in sparse graphs

This paper describes BBMCW, a new efficient exact maximum clique algorithm tailored for large sparse graphs which can be bit-encoded directly into memory without a heavy performance penalty. These graphs occur in real-life problems when some form of locality may be exploited to reduce their scale. One such example is correspondence graphs derived from data association problems. The new algorithm is based on the bit-parallel kernel used by the BBMC family of published exact algorithms. BBMCW employs a new bitstring encoding that we denote ‘watched’, because it is reminiscent of the ‘watched literal’ technique used in satisfiability and other constraint problems. The new encoding reduces the number of spurious operations computed by the BBMC bit-parallel kernel in large sparse graphs. Moreover, BBMCW also improves on bound computation proposed in the literature for bit-parallel solvers. Experimental results show that the new algorithm performs better than prior algorithms over data sets of both real and synthetic sparse graphs. In the real data sets, the improvement in performance averages more than two orders of magnitude with respect to the state-of-the-art exact solver IncMaxCLQ.     

Efficient Partitioning Method for Optimizing the Compression on Array Data

Array partitioning is an important research problem in array management area, since the partitioning strategies have important influence on storage, query evaluation, and other components in array management systems. Meanwhile, compression is highly needed for the array data due to its growing volume. Observing that the array partitioning can affect the compression performance significantly, this paper aims to design the efficient partitioning method for array data to optimize the compression performance. As far as we know, there still lacks research efforts on this problem. In this paper, the problem of array partitioning for optimizing the compression performance (PPCP for short) is firstly proposed. We adopt a popular compression technique which allows to process queries on the compressed data without decompression. Secondly, because the above problem is NP-hard, two essential principles for exploring the partitioning solution are introduced, which can explain the core idea of the partitioning algorithms proposed by us. The first principle shows that the compression performance can be improved if an array can be partitioned into two parts with different sparsities. The second principle introduces a greedy strategy which can well support the selection of the partitioning positions heuristically. Supported by the two principles, two greedy strategy based array partitioning algorithms are designed for the independent case and the dependent case respectively. Observing the expensive cost of the algorithm for the dependent case, a further optimization based on random sampling and dimension grouping is proposed to achieve linear time cost. Finally, the experiments are conducted on both synthetic and real-life data, and the results show that the two proposed partitioning algorithms achieve better performance on both compression and query evaluation.     

基于三维行为关系图的模型一致性检测方法

在业务流程模型的相似性分析过程中,有时会出现环结构。已有的方法一般不考虑环结构,忽略了环结构对模型一致性分析的影响。以Petri网的多重变迁集为基础,提出一种新的一致性度测量方法。首先通过分析5种行为序列关系来刻画Petri网的变迁之间的相互关系,给出了三维行为关系图的概念;然后对Petri网的三维行为关系图间的关系进行研究,提出了基于Petri网的三维行为关系图的一致性检测方法。理论分析和实例测试均表明了该方法的有效性。     

Connective fault tolerance in multiple bus systems

We present an efficient approach to characterizing the fault tolerance of multiprocessor systems that employ multiple shared buses for interprocessor communication. Of concern is connective fault tolerance, which is defined as the ability to maintain communication between any two fault-free processors in the presence of faulty processors, buses, or processor-bus links. We introduce a model called processor-bus-link (PBL) graphs to represent a multiple-bus system's interconnection structure. The model is more general than previously proposed models, and has the advantages of simple representation, broad application, and the ability to model partial bus failures. The PBL graph implies a set of component adjacency graphs that highlights various connectivity features of the system. Using these graphs, we propose a method for analyzing the maximum number of faults a multiple-bus system can tolerate, and for identifying every minimum set of faulty components that disconnects the processors of the system. We also analyze the connective fault tolerance of several proposed multiple-bus systems to illustrate the application of our method     

Parameterization of the discriminant set of a polynomial

The discriminant set of a real polynomial is studied. It is shown that this set has a complex hierarchical structure and consists of algebraic varieties of various dimensions. A constructive algorithm for a polynomial parameterization of the discriminant set in the space of the coefficients of the polynomial is proposed. Each variety of a greter dimension can be geometrically considered as a tangent developable surface formed by one-dimensional linear varieties. The role of the directrix is played by the component of the discriminant set with the dimension by one less on which the original polynomial has a single multiple root and the other roots are simple. The relationship between the structure of the discriminant set and the partitioning of natural numbers is revealed. Various algorithms for the calculation of subdiscriminants of polynomials are also discussed. The basic algorithms described in this paper are implemented as a library for Maple.     

An efficient integer programming formulation for the assignment of base stations to controllers in cellular networks

In mobile networks, the assignment of base stations to controllers when planning the network has a strong impact on network performance. In a previous paper, the authors formulated the assignment of base stations to packet controllers in GSM-EDGE Radio Access Network (GERAN) as a graph partitioning problem, which was solved by a heuristic method. In this paper, an exact method is presented to find optimal solutions that can be used as a benchmark. The proposed method is based on an effective re-formulation of the classical integer linear programming model of the graph partitioning problem, which is solved by the branch-and-cut algorithm in a commercial optimization package. Performance assessment is based on an extensive set of problem instances built from data of a live network. Preliminary analysis shows some properties of the graphs in this problem justifying the limitations of heuristic approaches and the need for more sophisticated methods. Results show that the proposed method outperforms classical heuristic algorithms used for benchmarking, even under runtime constraints. Likewise, it improves the efficiency of exact methods previously applied to similar problems in the cellular field.     

基于分片的XML快速结构连接算法

结构连接作为XML查询的重要部分,对查询性能来说起着非常重要的作用.目前有几种结构连接算法已经被提出,例如Stack-Tree、XR-tree.这些算法主要集中在节点之间关系的确定上.与之不同,作者从分片的角度去解决结构连接问题,首先把节点间的关系引申到分片之间的关系,从而得出各分片之间的一些性质,再利用分片间的性质来提高结构连接操作的性能.文中提出了一种基于分片的结构连接算法和两种优化方法,实验表明该算法在性能上要优于Stack-Tree算法和XR-tree算法.设计了一个简单而又高效的索引结构来存储分片结果,实验结果表明该索引结构的维护代价要小于XR-tree的维护代价.     

Minimal functional routes in directed graphs with dependent edges

Graphs are mathematical structures used to model a set of objects and the relations between them. One of the basic concepts of graph theory, the path, has wide real‐world applications. In classic graph models, edges ending at a node are assumed to be independent. However, many real graphs/networks can only be correctly described by considering a dependency among nodes or edges. Paths in such graphs may not be functional if the conditional dependency is ignored. In this study, we investigate the routing problem in directed graphs with dependent edges represented by general graph models as alternatives to hypergraphs. We define a minimal functional route (MFR) as a minimal set of nodes and edges that can independently perform information transfer between two given nodes, and formulate the determination of MFRs as a graph search problem. A depth‐first‐search (DFS) top‐down algorithm, an iterative integer linear programming (ILP) bottom‐up algorithm, and a subgraph‐growing bottom‐up algorithm are devised subsequently to solve this problem. Numerical experiments verify the effectiveness of the algorithms. The defined MFR problem and the proposed algorithms are expected to find many practical applications.     

Identification of multi-class linear and nonlinear systems

An algorithm for the identification of multi-class systems which can be described by a class of models over different operating regions is presented. The algorithm involves partitioning the raw data set using discriminant functions followed by parameter estimation. An orthogonal least squares algorithm coupled with a backward elimination procedure is employed for the parameter estimation and data partitioning processes. Provided the data elements are linearly separable, the proposed algorithm will correctly partition the data into the respective classes; parameter estimation algorithms can then be applied to estimate the models associated with each different class. Simulation studies are included to illustrate the algorithm