程序控制流图自动生成的算法

运用程序控制流图,可以方便地度量程序的逻辑复杂度,确定软件测试中控制结构独立路径的基本集合。文章提出了根据程序设计的伪码,自动生成程序控制流图的数据结构和详细的算法,为进行控制优化、软件基本路径测试以及程序控制相关性分析提供了良好的基础。     

面向时序图数据的快速环枚举算法

时序图数据是一类边上带有时间戳信息的图数据.在时序图数据中,时序环是边满足时间戳递增约束的回路.时序环枚举在现实中有着很多应用,它可以帮助挖掘金融网络中的欺诈行为.此外,研究时序环的数量对于刻画不同时序图的特性也有重要作用.基于2018年由RohitKumar等人提出的时序环枚举算法(2SCENT算法),提出一种通过添加环路信息来削减搜索空间的新型时序环枚举算法.所提出的算法为一个两阶段的算法:1)首先,通过遍历原图获得所有可能会形成环路的节点,以及相应的时间和长度信息;2)然后,利用以上信息进行动态深度优先搜索,挖掘所有的满足约束条件的环.在4个不同的真实时序图数据集上进行了大规模的实验,并以2SCENT算法作为基准对算法进行了对比.实验结果表明,所提出的算法较之前最好的2SCENT算法要快50%以上.     

最小谣传图的一个有效算法

谣传是信息网络中结点之间的一种常见的、重要的信息交换方式，在谣传过程中，每一个结点都得到ｋ个结点的信息，这个概念在计算机网络及其它信息、通信网络的设计中有着重要的意义，本文把“权”的概念引入到谣传问题中来，从而定义了最小谣传图，并给出了最小谣传图的一个好算法。     

多连通域Voronoi图的算法及数据存储

通过对两种主要单连通域Voronoi图算法的剖析,改进初始化算法和数据结构,得到便于工程应用的单连通域Voronoi算法,并将波阵面传播的思想扩展应用到求多连通域的Voronoi图,形成新的多连通域问题算法,从而解决了工程中特别是分层制造技术中Voronoi图应用的一般性问题.     

求有效极小（受控）可重复向量的一个算法

文献［１］基于有效（受控）可重复向量，给出了判定一个标准Ｐｅｔｒｉ网产生的语言分别为正规语言或上下文无关语言的充要条件，然而，求取一个标准Ｐｅｔｒｉ网的有效（受控）可重复向量是着定网语言属型的前提条件，文献［１］没有给出求取它们的方法，本文提出一个算法，使得文献［１］判据可实现，此外，作为副产品，同时产生出网的所有极小Ｔ－不变量以及公平性判定的实现。     

求解连通图关节点的一种新的思考方法

引入图以及图的深度优先搜索数据结构定义,在图的深度优先搜索定义的基础上，讨论了从深度优先搜索定义出发，查找连通图的全部关节点的算法。     

BB图的枚举特征

在并发程序复杂性度量研究中,我们曾定义了一种B图,用以作为Ada并发程序中一种会合关系的模型。我们将B图推广到BB图。n节点BB图是在n个节点的串联树上再添加若干条边,其约束条件是：每个节点的入度不大于二,每个节点的出度也不大于二。给出BB图的若干若干枚举特征,指出同第二类Stiding数的密切关系。     

一种高效的凸连通子图枚举算法

在可配置处理器的定制指令设计过程中,需要提取热点代码数据流图的凸连通子图.为实现子图的快速枚举,对有向无环图内的凸子图特性进行了研究.根据凸子图特性和节点邻接关系,提出了一种AS(adjacent search) 算法用于枚举有向无环图内满足I/O端口约束的凸连通子图.实验数据显示,AS算法比现有算法具有更高的效率,加速比可达10～1000X.当现有算法因数据流图规模较大而失效时,应用AS算法仍能成功完成子图枚举.     

Enumerating all connected maximal common subgraphs in two graphs

We represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem. We have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs. These algorithms are based on variants of the Bron–Kerbosch algorithm. In this paper we explain the transformation of the maximal common subgraph problem into the clique problem. We give a short summary of the variants of the Bron–Kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs. After introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs. The results show the drastical reduction of the runtimes for the new algorithms.     

Enumerating all spanning trees for pairwise comparisons

Determining the most suitable prioritization method for pairwise comparisons remains an open problem. This paper proposes a method based on the generation of all possible preferences from a set of judgments in pairwise comparisons. A concept of pivotal combination is introduced using a graph-theoretic approach. A set of preferences is generated by enumerating all spanning trees. The mean of these preferences is proposed as a final priority vector, and variance gives a measure of inconsistency. The proposed method provides a way of ordering objects according to a voting scheme. The proposed method is also applicable to incomplete sets of pairwise comparisons without modification, unlike other popular methods which require intermediate steps to estimate missing judgments.     

Separators in Graphs with Negative and Multiple Vertex Weights

A separator theorem for a class of graphs asserts that every graph in the class can be divided approximately in half by removing a set of vertices of specified size. Nontrivial separator theorems hold for several classes of graphs, including graphs of bounded genus and chordal graphs. We show that any separator theorem implies various weighted separator theorems. In particular, we show that if the vertices of the graph have real-valued weights, which may be positive or negative, then the graph can be divided exactly in half according to weight. If k unrelated sets of weights are given, the graph can be divided simultaneously by all k sets of weights. These results considerably strengthen earlier results of Gilbert, Lipton, and Tarjan: (1) for k=1 with the weights restricted to being nonnegative, and (2) for k>1 , nonnegative weights, and simultaneous division within a factor of (1+ε ) of exactly in half. Received November 21, 1995; revised October 30, 1997.     

An Algorithm for Enumerating All Spanning Trees of a Directed Graph

We present an O(NV + V ³ ) time algorithm for enumerating all spanning trees of a directed graph. This improves the previous best known bound of O(NE + V+E) [1] when V ² =o(N) , which will be true for most graphs. Here, N refers to the number of spanning trees of a graph having V vertices and E edges. The algorithm is based on the technique of obtaining one spanning tree from another by a series of edge swaps. This result complements the result in the companion paper [3] which enumerates all spanning trees in an undirected graph in O(N+V+E) time. Received September 11, 1997; revised March 6, 1998.     

有向无环图的高效归约算法

将一个应用程序部署到给定的片上网络上执行时,需要将应用程序中的每一个子任务都指派给片上网络中的一个节点执行。该问题一般被建模成一组子任务作为顶点的有向无环图,任务在片上网络上的部署过程就等同于一个有向无环图的顶点向一个片上网络拓扑映射的过程。而随着应用程序和片上网络规模的增大,计算一个最优的映射方案是典型的难解问题。为了加速有向无环图到片上网络拓扑的映射过程,提出了有向无环图的归约算法,使归约后的图中的顶点数量尽可能地与给定片上网络中的节点数量相同。提出的图归约算法可以有效地识别出所有可归约子图,这些可归约子图可被归约为单一顶点。新算法的适用范围从嵌套图扩展到了任意图,并且拥有与原算法相同的复杂度量级。还提出了一种并行化的算法思想来加速可归约子图的搜索过程。     

Efficient Parallel Graph Algorithms for Coarse-Grained Multicomputers and BSP

In this paper we present deterministic parallel algorithms for the coarse-grained multicomputer (CGM) and bulk synchronous parallel (BSP) models for solving the following well-known graph problems: (1) list ranking, (2) Euler tour construction in a tree, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, and (7) 2-edge connectivity and biconnectivity (testing and component computation). The algorithms require O(log p) communication rounds with linear sequential work per round (p = no. processors, N = total input size). Each processor creates, during the entire algorithm, messages of total size O(log (p) (N/p)) . The algorithms assume that the local memory per processor (i.e., N/p ) is larger than p ^ε , for some fixed ε > 0 . Our results imply BSP algorithms with O(log p) supersteps, O(g log (p) (N/p)) communication time, and O(log (p) (N/p)) local computation time. It is important to observe that the number of communication rounds/ supersteps obtained in this paper is independent of the problem size, and grows only logarithmically with respect to p . With growing problem size, only the sizes of the messages grow but the total number of messages remains unchanged. Due to the considerable protocol overhead associated with each message transmission, this is an important property. The result for Problem (1) is a considerable improvement over those previously reported. The algorithms for Problems (2)—(7) are the first practically relevant parallel algorithms for these standard graph problems. Received July 5, 2000; revised April 16, 2001.     

基于混合图像分割与梯度算法的发光物体图像重建技术研究

传统的图像重建算法存在光源分布不均以及噪声干扰等问题,导致图像重建效果差。针对该问题,提出了一种改进的混合图割算法和梯度算法的发光体图像重建技术。算法首先采用图像分割算法得到在未知先验条件的情况下的发光源情况;然后利用不同的梯度算法,根据重建状态得到发光源准确的分布情况;最后利用内部光源的多级网络提高计算速度和重建的准确性。仿真实验结果表明,本方法即使在存在检测噪声和模型结构误差的情况下,仍然能够得到很好的重建性能,具有较高的实际应用价值。     

面向高通量计算机的图算法优化技术

随着互联网技术的蓬勃发展,图数据的规模呈爆炸式增长.如何高效地处理大规模图数据逐渐成为工业界和学术界关注的焦点.宽度优先搜索算法是解决图遍历问题的经典算法,也是Graph500基准的核心测试程序之一.高通量计算机采用ARM架构的众核体系结构,具有高并发、强实时、低功耗等适于大数据计算的特点.在单节点上,BFS算法的优化已取得一系列进展,首先对现有的优化技术进行系统的介绍,并在此基础上提出2种面向高通量计算机的优化手段,通过减少冗余访存和提高缓存局部性,有效提高了算法的访存效率.通过这些优化手段,在高通量计算机上对BFS算法的性能进行了系统的评估.对于顶点规模为230的Kronecker图(顶点数为230,边数为234),优化后的BFS算法在高通量计算机上的平均性能为24.26 GTEPS.与两路x86架构服务器相比,单节点具有1.18倍的性能优势.在性能功耗比方面,高通量计算机的结果为181.04 MTEPS/W.在2019年6月份的Green Graph500面向大数据集的排行榜上取得第2名的成绩.综上,高通量计算机的高并发和低功耗等特点非常适合处理大规模图计算等数据密集型应用.     

Graph separators: a parameterized view

Graph separation is a well-known tool to make (hard) graph problems accessible to a divide-and-conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop fixed parameter algorithms for many well-known NP-hard (planar) graph problems. We coin the key notion of glueable select&verify graph problems and derive from that a prospective way to easily check whether a planar graph problem will allow for a fixed parameter algorithm of running time for constant c. One of the main contributions of the paper is to exactly compute the base c of the exponential term and its dependence on the various parameters specified by the employed separator theorem and the underlying graph problem. We discuss several strategies to improve on the involved constant c.     

求解图的最大团的一种算法

图的最大团问题是一个著名的ＮＰ－完全问题．现有求解图的最大团的算法或者只适用于某些特殊的图,或者需要指数级时间代价,效率较低．以图的区间表示的概念为基础,提出了一种求解最大团的算法．该算法能够适用于任意的简单图,并且在一定的条件下,该算法只需要多项式时间就可以完成运行.