一种新的分布性保持方法

分布性保持是多目标进化算法主要目标之一. 然而通常维护方法的性能与运行时间存在矛盾. 提出一种基于最小生成树的分布性维护方法. 利用最小生成树中的度数和边长对个体密度进行估计, 使低度数的边界个体和长边长的低密度个体得到了保留. 另外, 一次性选择个体进入下代种群, 避免了每移出一个个体就需要对个体密度进行调整的操作. 通过5个测试问题和4个方面的测试标准, 与3个著名的算法进行比较实验, 结果表明该方法在以较快速度对种群进行维护的同时, 拥有良好的分布性.     

An analysis of diversity measures

Diversity among the base classifiers is deemed to be important when constructing a classifier ensemble. Numerous algorithms have been proposed to construct a good classifier ensemble by seeking both the accuracy of the base classifiers and the diversity among them. However, there is no generally accepted definition of diversity, and measuring the diversity explicitly is very difficult. Although researchers have designed several experimental studies to compare different diversity measures, usually confusing results were observed. In this paper, we present a theoretical analysis on six existing diversity measures (namely disagreement measure, double fault measure, KW variance, inter-rater agreement, generalized diversity and measure of difficulty), show underlying relationships between them, and relate them to the concept of margin, which is more explicitly related to the success of ensemble learning algorithms. We illustrate why confusing experimental results were observed and show that the discussed diversity measures are naturally ineffective. Our analysis provides a deeper understanding of the concept of diversity, and hence can help design better ensemble learning algorithms. Editor: Tom Fawcett     

Algorithms for Computing the QR Decomposition of a Set of Matrices with Common Columns

The QR decomposition of a set of matrices which have common columns is investigated. The triangular factors of the QR decompositions are represented as nodes of a weighted directed graph. An edge between two nodes exists if and only if the columns of one of the matrices is a subset of the columns of the other. The weight of an edge denotes the computational complexity of deriving the triangular factor of the destination node from that of the source node. The problem is equivalent to constructing the graph and finding the minimum cost for visiting all the nodes. An algorithm which computes the QR decompositions by deriving the minimum spanning tree of the graph is proposed. Theoretical measures of complexity are derived and numerical results from the implementation of this and alternative heuristic algorithms are given.     

矩阵形网络图最小生成树算法的优化

最小连接问题在网络优化中有广泛的应用,找到快速有效的算法来构造最小生成树是解决问题的关键。该文提出了一种构造算法,在存储结构和排序方法两方面进行了改进。从理论上分析了算法的计算复杂度,并实际测试了算法运行时间。结果表明该算法较现有算法有了很大提高。     

A linear algorithm for analysis of minimum spanning and shortest-path trees of planar graphs

We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a single-source shortest-path tree to changes in edge costs, and to analyze the sensitivity of a minimum-cost network flow. The algorithm is simple and practical. It uses the properties of a planar embedding, combined with a heap-ordered queue data structure.This research was partially supported by Office of Naval Research Grant N00014-87-K-0467 and National Science Foundation Grant CCR-8610181.This research was done while the author was at the Department of Computer Science, Princeton University, Princeton, NJ 08544, USA.This research was done while the author was at the Department of Computer Science, Stanford University, Stanford, CA 94305, USA.     

Optimal parallel algorithms for multiple updates of minimum spanning trees

Parallel updates of minimum spanning trees (MSTs) have been studied in the past. These updates allowed a single change in the underlying graph, such as a change in the cost of an edge or an insertion of a new vertex. Multiple update problems for MSTs are concerned with handling more than one such change. In the sequential case multiple update problems may be solved using repeated applications of an efficient algorithm for a single update. However, for efficiency reasons, parallel algorithms for multiple update problems must consider all changes to the underlying graph simultaneously. In this paper we describe parallel algorithms for updating an MST whenk new vertices are inserted or deleted in the underlying graph, when the costs ofk edges are changed, or whenk edge insertions and deletions are performed. For multiple vertex insertion update, our algorithm achieves time and processor bounds ofO(log n·logk) and nk/(logn·logk), respectively, on a CREW parallel random access machine. These bounds are optimal for dense graphs. A novel feature of this algorithm is a transformation of the previous MST andk new vertices to a bipartite graph which enables us to obtain the above-mentioned bounds.     

基于禁忌搜索的聚类簇数目估算算法

本文提出一种基于禁忌搜索的聚类算法,能自动估计数据集的正确的聚类簇数目,其数据对象既可是紧凑球型分布,也可是非紧凑球型分布,或皆具两者。该算法包括三个阶段：最小生成树聚类、聚类簇重组和禁忌搜索优化。实验结果表明,所提出的算法可行、有效。     

Optimal parallel verification of minimum spanning trees in logarithmic time

We present the first optimal parallel algorithms for the verification and sensitivity analysis of minimum spanning trees. Our algorithms are deterministic and run inO(logn) time and require linear-work in the CREW PRAM model. These algorithms are used as a subroutine in the linear-work randomized algorithm for finding minimum spanning trees of Cole, Klein, and Tarjan. Research partially supported by a National Science Foundation Graduate Fellowship and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, Grant No. NSF-STC88-09648. Research at Princeton University was partially supported by the National Science Foundation, Grant No. CCR-8920505, the Office of Naval Research, Contract No. N00014-91-J-1463, and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, Grant No. NSF-STC88-09648.     

Efficient determination of the k most vital edges for the minimum spanning tree problem

We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree. We propose for this problem an explicit enumeration algorithm whose complexity, when compared to the current best algorithm, is better for general k but very slightly worse for fixed k. More interestingly, unlike in the previous algorithms, we can easily adapt our algorithm so as to transform it into an implicit enumeration algorithm based on a branch and bound scheme. We also propose a mixed integer programming formulation for this problem. Computational results show a clear superiority of the implicit enumeration algorithm both over the explicit enumeration algorithm and the mixed integer program.     

Two graph theory based methods for identifying the pectoral muscle in mammograms

Two image segmentation methods based on graph theory are used in conjunction with active contours to segment the pectoral muscle in screening mammograms. One method is based on adaptive pyramids (AP) and the other is based on minimum spanning trees (MST). The algorithms are tested on a public data set of mammograms and results are compared with previously reported methods. In 80% of the images, the boundary of the segmented regions has average error less than 2 mm. In 82 of 84 images, the boundary of the pectoral muscle found by the AP algorithm has average error less than 5 mm.     

基于Prim算法的通信网络架设仿真研究与应用

为了更好地提高通信网络架设实际问题的工作效率,进行了通信网络架设过程的仿真研究.通过算法的比较选择,对通信网络构架进行了动态规划.以最小代价生成树普里母算法为研究基础,采用数据结构的分析方法进行假设论证.文中结合通信网络构架的实际具体问题,讨论了网络规划中线路权重的选取方法,并在C语言环境下设计了适用于各个城市网络的节点-支路邻接表的数据存储结构.经实例验证,该方法具有计算速度快的优点并有效减少资源浪费,不仅可以保证通信网络架设工作效率,而且可以有效提高通信网络架设经济效益.     

Detection and typification of linear structures for dynamic visualization of 3D city models

Cluttering is a fundamental problem in 3D city model visualization. In this paper, a novel method for removing cluttering by typification of linear building groups is proposed. This method works in static as well as dynamic visualization of 3D city models. The method starts by converting building models in higher Levels of Details (LoDs) into LoD1 with ground plan and height. Then the Minimum Spanning Tree (MST) is generated according to the distance between the building ground plans. Based on the MST, linear building groups are detected for typification. The typification level of a building group is determined by its distance to the viewpoint as well as its viewing angle. Next, the selected buildings are removed and the remaining ones are adjusted in each group separately. To preserve the building features and their spatial distribution, Attributed Relational Graph (ARG) and Nested Earth Mover’s Distance (NEMD) are used to evaluate the difference between the original building objects and the generalized ones. The experimental results indicate that our method can reduce the number of buildings while preserving the visual similarity of the urban areas.     

Optimal algorithms for the single and multiple vertex updating problems of a minimum spanning tree

The vertex updating problem for a minimum spanning tree (MST) is defined as follows: Given a graphG=(V, E _G) and an MSTT forG, find a new MST forG to which a new vertexz has been added along with weighted edges that connectz with the vertices ofG. We present a set of rules that produce simple optimal parallel algorithms that run inO(lgn) time usingn/lgn EREW PRAM processors, wheren=¦V¦. These algorithms employ any valid tree-contraction schedule that can be produced within the stated resource bounds. These rules can also be used to derive simple linear-time sequential algorithms for the same problem. The previously best-known parallel result was a rather complicated algorithm that usedn processors in the more powerful CREW PRAM model. Furthermore, we show how our solution can be used to solve the multiple vertex updating problem: Update a given MST whenk new vertices are introduced simultaneously. This problem is solved inO(lgk·lgn) parallel time using (k·n)/(lgk·lgn) EREW PRAM processors. This is optimal for graphs having (kn) edges.Part of this work was done while P. Metaxas was with the Department of Mathematics and Computer Science, Dartmouth College.     

Prim算法在架设通信网络系统中的应用

通信网络系统架设属于典型的图论优化问题,针对通信网络系统的特点,抽象问题,简化模型,以通信网络系统架设费用最小为优化目标,应用Prim算法进行通信网络系统架设模型研究.首先简述了七城市之间架设通信网络系统问题,然后应用数学建模知识对隐含在该问题中的图论模型进行抽象研究,进而构造问题的数学模型,最后应用Prim算法设计了该通信网络系统架设的实现流程及相应代码的编写.程序执行结果表明:准确构建了问题的数学模型及应用Prim算法正确求解了该数学模型;并且权值因子的可变性使得该程序具有较强的通用性,易于在实际中使用.     

一种分布式数据库多元连接查询优化算法及改进

论文对于分布式数据库中的多元连接查询提出了一种优化算法。该算法产生的操作序列具有全局优化特征。在远程网中,采用最小生成树算法,生成最佳的连接序对能使得总的代价达到最小。而在局域网中,采用改进的最小生成树算法,生成尽可能多的并行连接序对,最大程度地应用并行性,使得响应时间最小。     

A distributed multicast routing algorithm for real-time applications in wide area networks

The problem of constructing a minimal cost multicast routing tree (MRT) with delay constraints in wide area networks (WAN) is considered. A new distributed token-passing based algorithm that constructs a sub-optimal MRT satisfying given delay constraints for all members in the multicast group is presented. In contrast with the previous works by Jia [A distributed algorithm of delay-bounded multicast routing for multimedia applications in wide area networks, IEEE/ACM Trans. Network. 6 (1998) 828–837] and several others [Y. Im, Y. Lee, S. Wi, Y. Choi, Delay constrained distributed multicast routing algorithm, Comput. Comm. 20 (1997) 60–66; X. Jia, Y. Zhang, N. Pissinou, K. Makki, A distributed multicast routing protocol for real-time multicast applications, Comput. Networks 31 (1999) 101–110; Q. Sun, H. Langendorfer, A distributed delay-constrained dynamic multicast routing algorithm, Telecommun. Systems 11 (1999) 47–58], in which cycles may occur, we show that the multicast routing network produced by our algorithm is indeed a tree, namely, cycle free. Also the success rate of our algorithm to find a feasible solution, if one exists, is guaranteed to be 100%, while Jia's algorithm is not. Furthermore, our algorithm is fault tolerant and can also adapt to cases where the multicast group members are allowed to join or leave the multicast session dynamically. Simulations have been conducted and the results show that the MRT generated by our algorithm has better performance compared to previous methods.     

Existence of solutions for a singular system of nonlinear fractional differential equations

In this paper, we establish the existence of positive solutions for a singular system of nonlinear fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Green’s function and its corresponding properties, we transform the derivative systems into equivalent integral systems. The existence is based on a nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

矩阵分析在Ad hoc网络生灭模型中的应用*

建立Ad hoc网络中路由发现过程中生成树的生灭过程模型,利用矩阵分析方法求解该过程的微分方程的解,在此基础上研究其概率分布、期望值,进而分析网络中节点的生灭及生成树的生灭。     

An empirical study of the structure of relevant keywords in a search engine using the minimum spanning tree

This paper provides a comprehensive study of the structure of relevant keywords in a search engine using the minimum spanning tree (MST) approach. In the process of constructing MST’s, we introduce a novel metric to measure a distance between keywords by applying an integration of the Pearson correlation and the query-based cosine similarity. From this work, we made several meaningful observations about the networks of relevant keywords. First, keyword networks in a search engine exhibit the small-world effect and the scale-free property. Second, only a few among relevant keywords in the order of popularity are positively correlated and there is no significantly positive or negative relationship for the rest of relevant keywords. Third, the degree of searching activity for relevant keywords varies depending on whether they are branded keywords or non-branded keywords as well as the characteristics of product categories. Fourth, the mean correlation coefficient for keyword impressions during slow season increases. Finally, both k_max and the betweenness centrality for high-involvement products are higher than those for low-involvement products.