Node overlap removal in clustered directed acyclic graphs

Graph drawing and visualization represent structural information as diagrams of abstract graphs and networks. An important subset of graphs is directed acyclic graphs (DAGs). This paper presents a new E-Spring algorithm, extended from the popular spring embedder model, which eliminates node overlaps in clustered DAGs. In this framework, nodes are modeled as non-uniform charged particles with weights, and a final drawing is derived by adjusting the positions of the nodes according to a combination of spring forces and repulsive forces derived from electrostatic forces between the nodes. The drawing process needs to reach a stable state when the average distances of separation between nodes are near optimal. We introduce a stopping condition for such a stable state, which reduces equilibrium distances between nodes and therefore results in a significantly reduced area for DAG visualization. It imposes an upper bound on the repulsive forces between nodes based on graph geometry. The algorithm employs node interleaving to eliminate any residual node overlaps. These new techniques have been validated by visualizing eBay buyer–seller relationships and has resulted in overall area reductions in the range of 45–79%.     

Recognition of directed acyclic graphs by spanning tree automata

In this paper, we study tree automata for directed acyclic graphs (DAGs). We define the movement of a tree automaton on a DAG so that a DAG is accepted by a tree automaton if and only if the DAG has a spanning tree accepted by the tree automaton. We call this automaton a spanning tree automaton. The NP-completeness of the membership problem of DAGs for spanning tree automata is shown. However, if inputs are restricted to series–parallel graphs or generalized series–parallel graphs, it is shown that the membership problem for spanning tree automata is solvable in linear time.     

基于遗传算法的有向无环图画图算法

在研究了现有画有向无环图的主要方法的基础上提出一种基于遗传算法的有向无环图画图算法,将一般有向无环图的画图问题转换为函数优化问题,用遗传算法求目标函数最优解的近似值。实验表明此算法具有算法统一、方法简单、容易实现、易于修改,并且具有自适应、自学习和易于并行化的特点。     

Convergent drawing for mutually connected directed graphs

Directed graphs are used to represent a variety of datasets, including friendship on social networking services (SNS), pathways of genes, and citations of research papers. Graph drawing is useful in representing such datasets. At the international conference on Information Visualization (IV), we have presented a convergent edge drawing and a node layout technique for tightly and mutually connected directed graphs. The edge drawing technique in the IV paper includes three features: ordinary bundling of edges connecting pairs of node clusters, convergence of multiple bundles that connect to the same node cluster, and shape adjustment of two bundles connecting the same pair of node clusters. In this paper, we present improved node layout and edge drawing techniques, which make our edge bundling more effective. This paper also introduces a case study with a directed paper citation graph dataset.vvvvv     

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。     

Topological sorts on DAGs

In this article, we will study the topological sorts of two directed acyclic graphs (DAGs) and the associated properties. More specifically, we will study under what conditions a certain single (or some, or every) topological sort(s) of a DAG can be extended into the topological sort(s) of another DAG. We first give the necessary and sufficient conditions for the problems. We then indicate that these problems are solvable either in linear time cost or in the same time cost as to compute the transitive closure.     

网格优化有向超图任务调度算法

任务调度是网格计算的一个重要部分.分析网格环境下任务调度的特点以及传统DAG图的优缺点,吸取有向超图的优点,将有向超图理论融合网格环境特征,建立了网格环境下的优化有向超图模型,并在此基础上通过网格优化有向超图的水平构形、标号及带宽计算实现任务对网格资源的映射与调度,提出网格优化有向超图任务调度算法GODHTS.模拟实验结果证明了该模型及其算法的有效性和优越性.     

Inference of structures of models of probabilistic dependences from statistical data

Problems of reconstruction of structures of probabilistic dependence models in the class of directed (oriented) acyclic graphs (DAGs) and mono-flow graphs are considered. (Mono-flow graphs form a subclass of DAGs in which the cycles with one collider are prohibited.) The technique of induced (provoked) dependences is investigated and its application to the identification of structures of models is shown. The algorithm “Collifinder-M” is developed that identifies all collider variables (i.e., solves an intermediate problem of reconstruction of the structure of a mono-flow model). It is shown that a generalization of the technique of induced dependences makes it possible to strengthen well-known rules of identification of orientation of edges in a DAG model. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 19–31, November–December 2005.     

On the granularity and clustering of directed acyclic task graphs

The authors consider the impact of the granularity on scheduling task graphs. Scheduling consists of two parts, the processors assignment of tasks, also called clustering, and the ordering of tasks for execution in each processor. The authors introduce two types of clusterings: nonlinear and linear clusterings. A clustering is nonlinear if two parallel tasks are mapped in the same cluster otherwise it is linear. Linear clustering fully exploits the natural parallelism of a given directed acyclic task graph (DAG) while nonlinear clustering sequentializes independent tasks to reduce parallelism. The authors also introduce a new quantification of the granularity of a DAG and define a coarse grain DAG as the one whose granularity is greater than one. It is proved that every nonlinear clustering of a coarse grain DAG can be transformed into a linear clustering that has less or equal parallel time than the nonlinear one. This result is used to prove the optimality of some important linear clusterings used in parallel numerical computing     

Run-Time Techniques for Exploiting Irregular Task Parallelism on Distributed Memory Architectures

Automatic scheduling for directed acyclic graphs (DAG) and its applications for coarse-grained irregular problems such as largen-body simulation have been studied in the literature. However, solving irregular problems with mixed granularities such as sparse matrix factorization is challenging since it requires efficient run-time support to execute a DAG schedule. In this paper, we investigate run-time optimization techniques for executing general asynchronous DAG schedules on distributed memory machines and discuss an approach for exploiting parallelism from commuting operations in the DAG model. Our solution tightly integrates the run-time scheme with a fast communication mechanism to eliminate unnecessary overhead in message buffering and copying. We present a consistency model incorporating the above optimizations, and take advantage of task dependence properties to ensure the correctness of execution. We demonstrate the applications of this scheme in sparse matrix factorizations and triangular equation solving for which actual speedups are difficult to obtain. We provide a detailed experimental study on Meiko CS-2 to show that the automatically scheduled code has achieved good performance for these difficult problems, and the run-time overhead is small compared to total execution times.     

A Visualization Framework and User Studies for Overloaded Orthogonal Drawings

Overloaded orthogonal drawing (OOD) is a recent graph visualization style specifically conceived for directed graphs. It merges the advantages of some popular drawing conventions like layered drawings and orthogonal drawings, and provides additional support for some common analysis tasks. We present a visualization framework called DAGView, which implements algorithms and graphical features for the OOD style. Besides the algorithm for acyclic digraphs, the DAGView framework implements extensions to visualize both digraphs with cycles and undirected graphs, with the additional possibility of taking into account user preferences and constraints. It also supports an interactive visualization of clustered digraphs, based on the use of strongly connected components. Moreover, we describe an experimental user study, aimed to investigate the usability of OOD within the DAGView framework. The results of our study suggest that OOD can be effectively exploited to perform some basic tasks of analysis in a faster and more accurate way when compared to other drawing styles for directed graphs.     

Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference

In this paper we will present a graph-transformation based method for the verification of heterogeneous first order logic (FOL) and Euler/Venn proofs. In previous work, it has been shown that a special collection of directed acyclic graphs (DAGs) can be used interchangeably with Euler/Venn diagrams in reasoning processes. Thus, proofs which include Euler/Venn diagrams can be thought of as proofs with DAGs where steps involving only Euler/Venn diagrams can be treated as particular DAG transformations. Here we will show how the characterization of these manipulations can be used to verify Euler/Venn proofs. Also, a method for verifying the use of heterogeneous Euler/Venn and FOL reasoning rules will be presented that is also based upon DAG transformations .     

Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference

In this paper we will present a graph-transformation based method for the verification of heterogeneous first order logic (FOL) and Euler/Venn proofs. It has been shown that a special collection of directed acyclic graphs (DAGs) can be used interchangeably with Euler/Venn diagrams in reasoning processes [4]. Thus, proofs which include Euler/Venn diagrams can be thought of as proofs with DAGs where steps involving only Euler/Venn diagrams can be treated as particular DAG transformations. In the work reported here, we will show how the characterization of these manipulations can be used to verify Euler/Venn proofs. Also, a method for verifying the use of heterogeneous Euler/Venn and FOL reasoning rules will be presented that is also based upon DAG transformations.     

利用遗传算法改进DAG绘制的方法

DAG图（Directed Acyclic Graph）广泛应用于数据库建模、工程设计等领域。DAG图一般用矩阵来存储,能够将矩阵存储的DAG图正确、美观地画出来,使得DAG图更直观,清晰,方便各种问题的分析和处理。DAG图的绘制包含分层、最小化边交叉数和删除哑结点。提出了基于遗传算法的分层和最小化边交叉数的方法和删除哑结点的启发式算法。实例结果表明提出的方法能有效解决DAG图绘制中的交叉点问题。     

Using graph parsing for automatic graph drawing

This paper presents a procedure for automatically drawing directed graphs. Our system, Clan-based Graph Drawing Tool (CG), uses a unique clan-based graph decomposition to determine intrinsic substructures (clans) in the graph and to produce a parse tree. The tree is given attributes that specify the node layout. CG then uses tree properties with the addition of “routing nodes” to route the edges. The objective of the system is to provide, automatically, an aesthetically pleasing visual layout for arbitrary directed graphs. The prototype has shown the strengths of this approach. The innovative strategy of clan-based graph decomposition is the first digraph drawing technique to analyze locality in the graph in two dimensions. The typical approach to drawing digraphs uses a single dimension, level, to arrange the nodes     

Indexing hierarchical structures using graph spectra

Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a low-dimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest-neighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate large-scale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of view-based 3D object recognition using shock graphs.     

基于LT+模型的社交网络影响力最大化研究

影响力最大化问题的目标是寻找社交网络中一组种子结点集合,在给定的传播模型下,使得这些结点最终传播的影响范围最大。Kempe和Kleinberg提出的贪心算法可以获得很好的影响范围,但是因复杂度太高而并不适用于大型社交网络。Chen和Yuan等人基于线性阈值(LT)模型提出了构造局部有向无环图的启发式算法,但是LT模型只考虑了邻居结点的直接影响力,忽略了结点之间存在的间接影响力。因此,在LT模型的基础上,结合网络中结点之间存在的间接影响力,提出了LT⁺影响力模型,并利用构造局部有向无环图的启发式算法求解LT⁺模型的影响力最大化,称为LT⁺DAG算法。真实数据集上的对比实验表明,LT⁺DAG算法具有更好的影响范围以及较好的可扩展性。     

大型数据库的模糊关联规则挖掘算法研究

为解决传统关联规则挖掘算法对大规模连续数据库进行挖掘时所产生的信息损失和效率低下等问题,给出一种改进的模糊关联规则挖掘算法,称为F-ARMVLQD算法。该算法利用模糊均值聚类算法解决离散属性间隔之间出现"尖锐边界"的问题,同时算法引入有向无环图和字节向量用以提高频繁项目集的计算效率,并吸取分区算法的优势,解决对该数据库挖掘时磁盘操作频繁的问题,整个算法只需扫描两次数据库。实验结果表明,该算法比传统算法具有更高的执行效率。     

基于混合粒子群算法的网格任务调度

减少分布式程序的执行时间是网格调度系统需要解决的重要问题。因分布式程序常建模为DAG图,故该问题又称异构DAG调度问题。在研究网格环境下的任务调度的基础上,提出了一种用于解决DAG任务调度问题的通用混合粒子群优化算法(Common Hybrid Particle Swarm Optimization),简称为CHPSO。该算法将问题的解(粒子)表示为任务的调度优先权向量,采用混合粒子群优化算法探索解空间。实验结果表明,在求解不含孤立点的单个DAG调度问题时,该算法所得解的调度长度仅为HEFT的90%～92%,求解质量与PSGA相当;在多张DAG图(含孤立节点)并发执行的网格环境中,该算法的调度性能明显优于PSGA及文中列出的其它演化计算方法。