基于原始对偶方法求解网络流量监测集算法

考虑网络节点的流守恒特性,网络流量的有效监测问题可抽象为求给定图G(V,E)的最小弱顶点覆盖集的问题和基于流划分的最小弱顶点覆盖集的问题,这是NP难的问题.首先分析了弱顶点覆盖集的约束关系,并给出了问题的整数规划形式.然后利用原始对偶方法构造了求解最小弱顶点覆盖集的近似算法,并分析了算法的比界为2.进一步分析了求解基于最大流划分的最小弱顶点覆盖集的近似算法.     

基于本体分割的语义图概要方法

语义图概要的目的是提取语义图的关键信息,形成原数据集的概要模型以解决大规模语义图的理解、查询、应用难题。为提升现有语义图概要方法效率,提出一种基于本体分割的概要方法。通过本体分割算法对语义图进行分割生成扩展子图。采用形式概念分析对每个扩展子图生成元素的偏序格（又称特征集格）。在此基础上,由所有子图的特征集格形成了原语义图的概要。在关联开放数据集和Berlin SPARQL Benchmark数据集上的实验结果表明,该方法具有较好的可扩展性,有效提高了概要方法的效率。     

Occupancy Problems with Pairwise Exclusion Constraints—An Aspect of Gait Enumeration

Abstract

Occupancy problems generally relate to ordered partitions of a set of objects. Often such partitions are subject to constraints which prevent certain types of objects from being placed in the same block of the partition. This paper is addressed to a particular problem of this type in which pairwise exclusion constraints are imposed. Specifically, what is sought is an enumeration of all possible partitions of a set of k pairs of objects such that no partition block contains two elements from the same pair. The results obtained are generally in the form of recursion relations. These relations have been solved completely for k ≤ 4 and partially for larger values of k. Numerical results are presented in the form of tables. An application of these tables to an enumeration of the theoretically possible gaits of bipeds, tripeds, and quadrupeds concludes the paper. It is found that the total number of such gaits is somewhat larger than previously suspected.     

A hybrid clustering algorithm

Clustering attempts to partition a dataset into a meaningful set of mutually exclusive clusters. It is known that sequential clustering algorithms can give optimal partitions when applied to an ordered set of objects. In this technical note, we explore how this approach could be generalized to partition datasets in which there is no natural sequential ordering of the objects. As such, it extends the application of sequential clustering algorithms to all sets of objects.     

Über Verfahren zur zweiseitigen Approximation inverser Elemente

In a partially ordered ring, a set of iterative methods is constructed in order to approximate the inverse of a given element, not necessarily positive or inverse-positive. Two sequences are generated both converging to the inverse. In addition the inverse is monotonously enclosed. The method of order four has the maximal efficiency index.     

Tight Results on Minimum Entropy Set Cover

In the minimum entropy set cover problem, one is given a collection of k sets which collectively cover an n-element ground set. A feasible solution of the problem is a partition of the ground set into parts such that each part is included in some of the k given sets. Such a partition defines a probability distribution, obtained by dividing each part size by n. The goal is to find a feasible solution minimizing the (binary) entropy of the corresponding distribution. Halperin and Karp have recently proved that the greedy algorithm always returns a solution whose cost is at most the optimum plus a constant. We improve their result by showing that the greedy algorithm approximates the minimum entropy set cover problem within an additive error of 1 nat =log ₂ e bits ≃1.4427 bits. Moreover, inspired by recent work by Feige, Lovász and Tetali on the minimum sum set cover problem, we prove that no polynomial-time algorithm can achieve a better constant, unless P = NP. We also discuss some consequences for the related minimum entropy coloring problem. G. Joret is a Research Fellow of the Fonds National de la Recherche Scientifique (FNRS).     

The Zermelo–Voronoi diagram: A dynamic partition problem

We consider a Voronoi-like partition problem in the plane for a given finite set of generators. Each element in this partition is uniquely associated with a particular generator in the following sense: an agent that resides within a set of the partition at a given time will arrive at the generator associated with this set faster than any other agent that resides anywhere outside this set at the same instant of time. The agent’s motion is affected by the presence of a temporally varying drift, which is induced by local winds/currents. As a result, the minimum time to a destination is not equivalent to the minimum distance traveled. This simple fact has important ramifications over the partitioning problem. It is shown that this problem can be interpreted as a Dynamic Voronoi Diagram problem, where the generators are not fixed, but rather they are moving targets to be reached in minimum time. The problem is solved by first reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation. We then extend the approach to solve the dual problem where the generators are the initial locations of a given set of agents distributed over the plane, such that each element in the partition consists of the terminal positions that can be reached by the corresponding agent faster than any other agent.     

基于模糊近似推理的Vague集双向近似推理方法

给出由有限论域上的Vague集导出的分拆真模糊向量和分拆非假模糊向量的定义。进而得到Vague集近似推理的真近似推理模型和非假近似推理模型。最后得到Vague集正向近似推理结论和逆向近似推理结论。实例表明这种Vague集双向近似推理方法是可行的。     

Bayesian Treed Models

When simple parametric models such as linear regression fail to adequately approximate a relationship across an entire set of data, an alternative may be to consider a partition of the data, and then use a separate simple model within each subset of the partition. Such an alternative is provided by a treed model which uses a binary tree to identify such a partition. However, treed models go further than conventional trees (e.g. CART, C4.5) by fitting models rather than a simple mean or proportion within each subset. In this paper, we propose a Bayesian approach for finding and fitting parametric treed models, in particular focusing on Bayesian treed regression. The potential of this approach is illustrated by a cross-validation comparison of predictive performance with neural nets, MARS, and conventional trees on simulated and real data sets.     

Polynomial-time algorithms for weighted efficient domination problems in AT-free graphs and dually chordal graphs

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient dominating set of minimum weight in a given vertex-weighted graph; the maximum weight efficient domination problem is defined similarly. We develop a framework for solving the weighted efficient domination problems based on a reduction to the maximum weight independent set problem in the square of the input graph. Using this approach, we improve on several previous results from the literature by deriving polynomial-time algorithms for the weighted efficient domination problems in the classes of dually chordal and AT-free graphs. In particular, this answers a question by Lu and Tang regarding the complexity of the minimum weight efficient domination problem in strongly chordal graphs.     

分区动态地形的一种时序模型

在分布式虚拟环境中,地形因实体作用发生变化.为了使各仿真节点的地形数据保持一致,需要对各节点变化的数据时序化.根据地形局部变化特点,构造了多分区动态地形的时序模型.模型把子区域地形几何数据定义为单纯复合形集,按地形变化时间顺序和空间关系组织成一个偏序集.模型支持地形变化数据动态添加,指定时刻的地形提取.实验表明,基于DAG表示的地形抽取算法利用变化数据间的空间关系提高了计算性能.     

Dominance-based rough set approach and knowledge reductions in incomplete ordered information system

Many methods based on the rough set to deal with incomplete information systems have been proposed in recent years. However, they are only suitable for the incomplete systems with regular attributes whose domains are not preference-ordered. This paper thus attempts to present research focusing on a complex incomplete information system—the incomplete ordered information system. In such incomplete information systems, all attributes are considered as criterions. A criterion indicates an attribute with preference-ordered domain. To conduct classification analysis in the incomplete ordered information system, the concept of similarity dominance relation is first proposed. Two types of knowledge reductions are then formed for preserving two different notions of similarity dominance relations. With introduction of the approximate distribution reduct into the incomplete ordered decision system, the judgment theorems and discernibility matrixes associated with four novel approximate distribution reducts are obtained. A numerical example is employed to substantiate the conceptual arguments.     

边赋权森林ω-路划分的O(n)算法

ω-路划分问题是路划分问题的一般化,它源于并行计算机系统、计算机网络与分布式控制系统等一类广播通信问题.设置最少的信息源节点,使得在指定的时间内将信息源节点所拥有的信息发送到其余节点,并且保证不同通信线路之间不得相交.从Hamilton路的NP-完全性不难看出,ω-路划分问题属于NP-完全问题.通过构造性证明技术,获得了边赋非负权路径、树和森林的ω-路划分问题的一些性质.分别提出了求解边赋非负权路径和边赋非负权树的ω-路划分问题的线性时间算法,讨论了算法的局部实现技术,详细地分析了这些算法的复杂度.以这两个算法为基础,提出了一个线性时间算法求解边赋非负权森林的ω-路划分问题.所提出的算法直观简明、操作容易,只需要较少的运行时间和较小的存储空间.     

Bicriterion cluster analysis

Cluster analysis is concerned with the problem of partitioning a given set of entities into homogeneous and well-separated subsets called clusters. The concepts of homogeneity and of separation can be made precise when a measure of dissimilarity between the entities is given. Let us define the diameter of a partition of the given set of entities into clusters as the maximum dissimilarity between any pair of entities in the same cluster and the split of a partition as the minimum dissimilarity between entities in different clusters. The problems of determining a partition into a given number of clusters with minimum diameter (i.e., a partition of maximum homogeneity) or with maximum split (i.e., a partition of maximum separation) are first considered. It is shown that the latter problem can be solved by the classical single-link clustering algorithm, while the former can be solved by a graph-theoretic algorithm involving the optimal coloration of a sequence of partial graphs, described in more detail in a previous paper. A partition into a given number of clusters will be called efficient if and only if there exists no partition into at most the same number of clusters with smaller diameter and not smaller split or with larger split and not larger diameter. Two efficient partitions are called equivalent if and only if they have the same values for the split and for the diameter.     

A note on hypergraph decomposition based on extended minimal sets

We discuss the problem of finding a partition of the nodes of a hypergraph Y with weighted arcs.Extended minimal sets (em-sets) of nodes are defined, intuitively corresponding to subsets of nodes of Y with a high number of inter-connections, and a partition of Y in em-sets is derived by a polynomial time algorithm. To show the nature of the partition, several properties of em-sets are proved. In particular, these sets can totally but not partially overlap. As an example of an application, the role of our partition in the field of VLSI design is briefly discussed. This research has been partially supported by a research grant of Italian Ministry for Public Education.     

Partitioning trees: Matching,domination, and maximum diameter

A matching and a dominating set in a graph G are related in that they determine diameter-bounded subtree partitions of G. For a maximum matching and a minimum dominating set, the associate partitions have the fewest numbers of trees. The problem of determining a minimum dominating set in an arbitrary graph G is known to be NP-complete. In this paper we present a linear algorithm for partitioning an arbitrary tree into a minimum number of subtrees, each having a diameter at mostk, for a givenk.Research supported in part by the National Science Foundation under Grant ENG 7902960.Research supported in part by the National Science Foundation under Grant STI 7902960.     

基于RBF神经网络的回归树学习算法

介绍了一种新的非参数回归RBF神经网络学习算法,该算法将RBF神经网络与回归树结合起来使用。回归树的基本思想是通过递归分割将输入空间划分为两部分,对函数进行逼近。由于每一次划分都与轴平行,因此可以用输入分向量满足的不等式来描述每一次划分,从而输入空间就变成了一个用超矩形构成的回归树(二叉树)。回归树的结点可以很容易地转换为径向基函数,通过对回归树结点的访问,可以选择出使网络达到最优的基函数集,形成最终的网络。该算法可以应用到函数逼近、图像处理等各方面。     

概念格与粗糙集的关系研究

概念格理论和粗糙集理论是两种不同的知识表示与知识发现的工具,都已被成功应用于许多领域.粗糙集理论的数据表现方式是信息系统,其研究基础是对象之间的等价关系;概念格理论的数据表现方式是形式背景,其研究基础是一种有序的层次结构--概念格.本文讨论了概念格理论与粗糙集理论之间的基本联系;重点分析了形式概念与等价类之间、概念格与分划之间的关系;证明了概念格与分划之间可以相互转换,给出了转换算法,并用例子加以说明.     

An intelligent,uncertainty driven aggregation scheme for streams of ordered sets

Data streams management has attracted the attention of many researchers during the recent years. The reason is that numerous devices generate huge amounts of data demanding an efficient processing scheme for delivering high quality applications. Data are reported through streams and stored into a number of partitions. Separation techniques facilitate the parallel management of data while intelligent methods are necessary to manage these multiple instances of data. Progressive analytics over huge amounts of data could be adopted to deliver partial responses and, possibly, to save time in the execution of applications. An interesting research domain is the efficient management of queries over multiple partitions. Usually, such queries demand responses in the form of ordered sets of objects (e.g., top-k queries). These ordered sets include objects in a ranked order and require novel mechanisms for deriving responses based on partial results. In this paper, we study a setting of multiple data partitions and propose an intelligent, uncertainty driven decision making mechanism that aims to respond to streams of queries. Our mechanism delivers an ordered set of objects over a number of partial ordered subsets retrieved by each partition of data. We envision that a number of query processors are placed in front of each partition and report progressive analytics to a Query Controller (QC). The QC receives queries, assigns the task to the underlying processors and decides the right time to deliver the final ordered set to the application. We propose an aggregation model for deriving the final ordered set of objects and a Fuzzy Logic (FL) inference process. We present a Type-2 FL system that decides when the QC should stop aggregating partial subsets and return the final response to the application. We report on the performance of the proposed mechanism through the execution of a large set of experiments. Our results deal with the throughput of the QC, the quality of the final ordered set of objects and the time required for delivering the final response.     

基于谱方法的无向赋权图剖分算法*

在多水平方法初始剖分阶段提出了一种基于谱方法的无向赋权图剖分算法SPWUG,给出了基于Lanczos迭代计算Laplacian矩阵次小特征值及特征向量的实现细节。SPWUG算法借助Laplacian矩阵次小特征值对应的特征向量,刻画了节点间相对距离,将基于非赋权无向图的Laplacian谱理论在图的剖分应用方面扩展到无向赋权图上,实现了对最小图的初始剖分。基于ISPD98电路测试基准的实验表明,SPWUG算法取得了一定性能的改进。实验分析反映了在多水平方法中,最小图上的全局近似最优剖分可能是初始图的局部最