无向图同构判定的并行算法

提出了一种判别无向图同构的方法,该方法根据无向图的邻接矩阵的特征值来判别出图的同构关系,而不需要其它附加信息。同时给出用Jacobi方法求出无向图的邻接矩阵的特征值的一种并行算法,它可以在分布式存储的多处理的多处理机上实现。实验结果表明,此方法是快速有效的,能在较短的运算时间内给出判断结果。     

A Heuristic Algorithm of Recognition of Isomorphism of Graphs

A heuristic polynomial algorithm is presented, which is used for the recognition of isomorphism of graphs and can be assigned to the group of methods that use local characteristic invariants of graphs. At each step, the behavior of the algorithm depends on information obtained at its previous steps. All the theorems stated are proved for a class of nonoriented graphs.     

任意图的同构判定算法:特征向量法

在构建有效描述任意图邻接矩阵的基础上,分别计算2个矩阵的特征值所对应的特征向量,并依据它们的极大无关组寻找可能的同构对应关系.通过逐一考查全体特征值,实现图同构的判定并确定同构图的顶点对应关系.随着判定规模增大及图对称性增强,与已有方法相比,文中方法具有更高的同构判定效率.实验结果表明,在多数情况下该方法是快捷有效的.     

Fast Parallel Reordering and Isomorphism Testing of k -Trees

In this paper two problems on the class of k -trees, a subclass of the class of chordal graphs, are considered: the fast reordering problem and the isomorphism problem. An O(log ² n) time parallel algorithm for the fast reordering problem is described that uses O(nk(n-k)/\kern -1ptlog n) processors on a CRCW PRAM proving membership in the class NC for fixed k . An O(nk(k+1)!) time sequential algorithm for the isomorphism problem is obtained representing an improvement over the O(n ² k(k+1)!) algorithm of Sekharan (the second author) [10]. A parallel version of this sequential algorithm is presented that runs in O(log ² n) time using O((nk((k+1)!+n-k))/log n) processors improving on a parallel algorithm of Sekharan for the isomorphism problem [10]. Both the sequential and parallel algorithms use a concept introduced in this paper called the kernel of a k -tree.     

一种基于图同构和单向置换的报文摘要构造算法

为了保护信息的机密性和完整性,该文给出了一种新的报文摘要构造算法,这种新算法是基于图同构的。为了把报文与图联系起来,采用了基于单向置换的报文摘要生成算法,并证明了对该算法而言,不存在多项式时间的概率算法来找到一个“冲突”。最后给出了类似于MD5算法的构造实例。     

Isomorphism for Graphs of Bounded Distance Width

In this paper we study the GRAPH ISOMORPHISM problem on graphs of bounded treewidth, bounded degree, or bounded bandwidth. GRAPH ISOMORPHISM can be solved in polynomial time for graphs of bounded treewidth, pathwidth, or bandwidth, but the exponent depends on the treewidth, pathwidth, or bandwidth. Thus, we look for special cases where ``fixed parameter tractable' polynomial time algorithms can be established. We introduce some new and natural graph parameters: the (rooted) path distance width, which is a restriction of bandwidth, and the (rooted) tree distance width, which is a restriction of treewidth. We give algorithms that solve GRAPH ISOMORPHISM in O(n ² ) time for graphs with bounded rooted path distance width, and in O(n ³ ) time for graphs with bounded rooted tree distance width. Additionally, we show that computing the path distance width of a graph is NP-hard, but both path and tree distance width can be computed in O(n ^k+1 ) time, when they are bounded by a constant k; the rooted path or tree distance width can be computed in O(ne) time. Finally, we study the relationships between the newly introduced parameters and other existing graph parameters. Received February 18, 1997; revised February 23, 1998.     

Fast Parallel Reordering and Isomorphism Testing of k -Trees

Abstract. In this paper two problems on the class of k -trees, a subclass of the class of chordal graphs, are considered: the fast reordering problem and the isomorphism problem. An O(log ² n) time parallel algorithm for the fast reordering problem is described that uses O(nk(n-k)/\kern -1ptlog n) processors on a CRCW PRAM proving membership in the class NC for fixed k . An O(nk(k+1)!) time sequential algorithm for the isomorphism problem is obtained representing an improvement over the O(n ² k(k+1)!) algorithm of Sekharan (the second author) [10]. A parallel version of this sequential algorithm is presented that runs in O(log ² n) time using O((nk((k+1)!+n-k))/log n) processors improving on a parallel algorithm of Sekharan for the isomorphism problem [10]. Both the sequential and parallel algorithms use a concept introduced in this paper called the kernel of a k -tree.     

一个关于Hamilton环(路)的多项式时间算法

该研究为Hamilton环路（道路）问题设计出了一个多项式时间算法,论证了它的正确性。根据该算法编制了程序,进行了大量的实例计算。文章公布了主要研究方法、过程、实验数据,以及粗略的算法步骤。详细的算法步骤和证明将在随后的论文中发表。由于Hamilton环路（道路）为著名的NP完全问题,而作者认为自己已彻底解决了NP复杂问题。     

Serial and Parallel Algorithms for (k,2)-Partite Graphs

We introduce a class of layered graphs which we call (k,2)-partite and which we argue are an interesting class because of several important applications. We show that testing for (k,2)-partiteness can be done efficiently both on sequential and parallel machines, by showing that membership is in NSPACE(log n) and in NC². We show that (k,2)-partite graphs have bounded path width. We then show that a particular NP-complete problem, namely Maximum Independent Set, is solvable in linear time on bounded pathwidth graphs if the path decomposition is included in the input. Finally, we show that the Maximum Independent Set problem is in NC² for (k,2)-partite graphs. We note that linear time solutions for certain NP-complete problems have been shown for a wider class of graphs, namely partial k-trees. Our linear time algorithm is somewhat simpler in structure. We conjecture that our techniques can be used on many NP-complete problems to yield efficient algorithms for (k,2)-partite graphs.     

A Linear Time Algorithm for the Arc Disjoint Menger Problem in Planar Directed Graphs

Given a graph G=(V,E) and two vertices s,t ∈ V , s\neq t , the Menger problem is to find a maximum number of disjoint paths connecting s and t . Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively. For planar graphs the edge disjoint Menger problem has been solved to optimality [W2], while the fastest algorithm for the arc disjoint version is Weihe's general maximum flow algorithm for planar networks [W1], which has running time \bf O (|V| log |V|) . Here we present a linear time, i.e., asymptotically optimal, algorithm for the arc disjoint version in planar directed graphs. Received August 1997; revised January 1999.     

Fermi架构下的时域高斯滤波并行算法

为提高图形图像处理中高斯滤波算法模块的计算速度,将高斯滤波与Fermi平台相结合,设计了一种高斯滤波时域的并行算法。数据测试结果显示,与基于CPU的实现相比,采用Fermi架构的GPU处理不仅可以得到误差精度小于0.0001的计算结果,而且可以取得较大的加速效果。在数据规模为512×112×128和滤波窗口大小为11的情况下能够达到约210倍的加速效果。     

A Linear Time Algorithm for L(2,1)-Labeling of Trees

An L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that |f(x)?f(y)|≥2 if x and y are adjacent and |f(x)?f(y)|≥1 if x and y are at distance 2, for all x and y in V(G). A k-L(2,1)-labeling is an L(2,1)-labeling f:V(G)→{0,…,k}, and the L(2,1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2, and tree is one of very few classes for which the problem is polynomially solvable. The running time of the best known algorithm for trees had been O(Δ ^4.5 n) for more than a decade, and an O(min{n ^1.75,Δ ^1.5 n})-time algorithm has appeared recently, where Δ and n are the maximum degree and the number of vertices of an input tree, however, it has been open if it is solvable in linear time. In this paper, we finally settle this problem by establishing a linear time algorithm for L(2,1)-labeling of trees. Furthermore, we show that it can be extended to a linear time algorithm for L(p,1)-labeling with a constant p.     

并联机器人力控制算法实时并行处理

对并联机器人力控制算法基于并行结构的计算进行了研究，设计了并行处理双机系统结构。采用文中的处理方法大大提高了并联机器人力控制算法的处理速度，保证了实时力控制，进而改善并联机器人的控制质量与性能。     

A Sequential Algorithm for Generating Random Graphs

We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence (d _i ) _i=1 ⁿ with maximum degree d _max?=O(m ^1/4?τ ), our algorithm generates almost uniform random graphs with that degree sequence in time O(md _max?) where $m=\frac{1}{2}\sum_{i}d_{i}We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence (d _i ) _i=1 ⁿ with maximum degree d _max=O(m ^1/4−τ ), our algorithm generates almost uniform random graphs with that degree sequence in time O(md _max) where m=\frac12?_id_im=\frac{1}{2}\sum_{i}d_{i} is the number of edges in the graph and τ is any positive constant. The fastest known algorithm for uniform generation of these graphs (McKay and Wormald in J. Algorithms 11(1):52–67, 1990) has a running time of O(m ² d _max²). Our method also gives an independent proof of McKay’s estimate (McKay in Ars Combinatoria A 19:15–25, 1985) for the number of such graphs.     

DAG任务图的一种调度算法

并行程序的调度技术是开发并行计算机系统的计算潜能的关键问题。本文讨论了4种典型的调度算法的缺陷，提出了一种新的调度算法CPFMBF，它采用的策略是：优先调度关键路径节点，其次调度b-level值大的节点，再次调度节点的关键路径影响度大的节点。对照分析及在几种具代表性的工程应用任务图上的实验结果证明CPFMBF算法的调度性能普遍好于其它算法。     

挖掘最大频繁模式的新方法

由于其内在的计算复杂性,挖掘密集型数据集的频繁模式完全集非常困难,解决方案之一是挖掘最大频繁模式集．该文在频繁模式完全集挖掘算法Opportune Project基础上,提出了挖掘最大频繁模式的新算法MOP．它采用宽度与深度优先相结合的混合搜索策略,能恰当地选择不同的支持集表示和投影方法,将闭合性剪裁和一般性剪裁相结合,并适时前窥,实现搜索与剪裁效率最优化．实验表明,MOP效率是MaxMiner的2～8倍,比MAFIA高2个数量级以上．     

Scheduling Parallel Task Graphs on (Almost) Homogeneous Multicluster Platforms

Applications structured as parallel task graphs exhibit both data and task parallelism and arise in many domains. Scheduling these applications efficiently on parallel platforms has been a long-standing challenge. In the case of a single homogeneous platform, such as a cluster, results have been obtained both in theory, i.e., guaranteed algorithms, and, in practice, i.e., pragmatic heuristics. Due to task parallelism, these applications are well suited for execution on distributed platforms that span multiple clusters possibly in multiple institutions. However, the only available results in this context are nonguaranteed heuristics. In this paper, we develop a scheduling algorithm, MCGAS, which is applicable to multicluster platforms that are almost homogeneous. Such platforms are often found as large subsets of multicluster platforms. Our novel contribution is that MCGAS computes task allocations so that a (tunable) performance guarantee is provided. Since a performance guarantee does not necessarily imply good average performance in practice, we also compare MCGAS with a recently proposed nonguaranteed algorithm. Using simulation over a wide range of experimental scenarios, we find that MCGAS leads to better average application makespans than its competitor.     

蔓叶线的一种并行生成算法

主要研究了著名的几何曲线——蔓叶线的一种并行生成算法,以Bresenham算法为基础,对蔓叶线的并行生成算法进行了分析和讨论。首先,从蔓叶线图像的一个已知点开始,根据递推公式逐点选择最靠近蔓叶线的像素点;然后引入并行机制生成蔓叶线的图像;最后,利用C#多线程模拟实现了该算法。模拟结果表明,这是关于蔓叶线图像的一种快速、高效的并行算法。