A fuzzy genetic algorithm for automatic orthogonal graph drawing

This paper reflects results of research related to developing a new methodology for automatic graph drawing based on applying genetic algorithms. The methodology has permitted the elaboration of a hybrid technique that combines the most popular, classical, topology-shape-metric approach to orthogonal drawings on the grid and a genetic algorithm that is directed, in its evolutionary process, at multicriteria decision making in a fuzzy environment. In the traditional use of the topology-shape-metric approach, a single fixed planar embedding is obtained in the planarization step. Thereafter this embedding is subjected to the orthogonalization and compaction steps. However, this sequence does not guarantee that the fixed planar embedding will generate a final drawing of a good quality. Moreover, every topology-shape-metric step is classified as a NP-hard problem, and choices as well as heuristics used in previous stages have a direct impact on subsequent ones. Taking this into account, the developed hybrid technique generates a greater number of planar embeddings by varying the order of edges’ insertion when forming the planar embeddings in planarization step. Thus, the problem is formulated as a permutation-based combinatorial optimization problem. The genetic algorithm is applied at the planarization step of the topology-shape-metric. This allows one to generate the population with the corresponding number of planar embeddings. Each planar embedding obtained in the planarization step is submitted to the orthogonalization and compaction. Their results serve for applying the procedures of multicriteria decision making in a fuzzy environment. Thus, in the evolutionary process, the genetic algorithm is able to select individuals, which provide more harmonious solutions (relatively of the solutions obtained with traditional applying the topology-shape-metric approach) from the point of view of the aesthetic criteria that are usually utilized at the three steps of automatic graph drawing. This is convincingly demonstrated by experimental results given in the paper.     

Looking for narrow interfaces in automatic differentiation using graph drawing

Automatic differentiation is a powerful technique for evaluating derivatives of functions given in the form of a high-level programming language such as Fortran, C, or C++. This technique is superior, in terms of accuracy, to numerical differentiation because it avoids the truncation error involved in divided difference approximations. In automatic differentiation, the program is treated as a potentially very long composition of elementary functions to which the chain rule of differential calculus is applied over and over again. Because of the associativity of the chain rule, there is room for different strategies computing the same numerical results but whose computational cost may vary significantly. Several strategies exploiting high-level structure of the underlying computer code are known to reduce computational cost as opposed to blindly applying automatic differentiation. An example includes “interface contraction” where one takes advantage of the fact that the number of variables passed between subroutines is small compared with the number of propagated directional derivatives. Unfortunately, these so-called narrow interfaces are not immediately available. The present study investigates the use of the VCG graph drawing tool to recognize narrow interfaces in the computational graph, a certain directed acyclic graph used to represent data dependences of variables in the underlying computer code.     

矿井通风网络图自动绘制技术研究

为了掌握目前矿井通风网络图自动绘制技术的研究现状以进行进一步的研究,从通风系统图网络结构信息的采集、网络通路的生成以及网络图的绘制等3个方面进行详细分析;阐述了这3个方面的研究内容和已经取得的研究成果,并且分析了目前这3个方面的研究存在的一些不足之处;最后指出了下一步的研究方向:引入人工智能,研究更高效的网络通路生成算法和怎样使网络图更简单美观。     

Three-dimensional graph drawing

Graph drawing research has been mostly oriented toward two-dimensional drawings. This paper describes an investigation of fundamental aspects of three-dimensional graph drawing. In particular we give three results concerning the space required for three-dimensional drawings. We show how to produce a grid drawing of an arbitraryn-vertex graph with all vertices located at integer grid points, in ann×2n×2n grid, such that no pair of edges cross. This grid size is optimal to within a constant. We also show how to convert an orthogonal two-dimensional drawing in anH×V integer grid to a three-dimensional drawing with volume. Using this technique we show, for example, that three-dimensional drawings of binary trees can be computed with volume . We give an algorithm for producing drawings of rooted trees in which thez-coordinate of a node represents the depth of the node in the tree; our algorithm minimizes thefootprint of the drawing, that is, the size of the projection in thexy plane. Finally, we list significant unsolved problems in algorithms for three-dimensional graph drawing. This work was performed as part of the Information Visualization Group(IVG) at the University of Newcastle. The IVG is supported in part by IBM Toronto Laboratory.     

Parametric graph drawing

A diagram is a drawing on the plane that represents a graph like structure, where nodes are represented by symbols and edges are represented by curves connecting pairs of symbols. An automatic layout facility is a tool that receives as input a graph like structure and is able to produce a diagram that nicely represents such a structure. Many systems use diagrams in the interaction with the users; thus, automatic layout facilities and algorithms for graphs layout have been extensively studied in the last years. We present a new approach in designing an automatic layout facility. Our approach is based on a modular management of a large collection of algorithms and on a strategy that, given the requirements of an application, selects a suitable algorithm for such requirements. The proposed approach has been used for designing the automatic layout facility of Diagram Server, a network server that offers to its clients several facilities for managing diagrams     

Online dynamic graph drawing

This paper presents an algorithm for drawing a sequence of graphs online. The algorithm strives to maintain the global structure of the graph and thus the user's mental map, while allowing arbitrary modifications between consecutive layouts. The algorithm works online and uses various execution culling methods in order to reduce the layout time and handle large dynamic graphs. Techniques for representing graphs on the GPU allow a speedup by a factor of up to 17 compared to the CPU implementation. The scalability of the algorithm across GPU generations is demonstrated. Applications of the algorithm to the visualization of discussion threads in Internet sites and to the visualization of social networks are provided.     

Algorithm recognition for programming tutoring based on flow graph parsing

Plan-recognition with template matching shows reasonable performance for recognizing general control structures. However, problems containing well-defined algorithms such as sorting and searching are difficult to recognize by the template-based methodology alone, because an algorithm is often highly optimized and therefore hard to divide into smaller meaningful units. Based on this observation, we propose an algorithm recognition methodology to augment the plan-recognition approach.Our algorithm recognition approach is based on the flow graph parsing which performs a partial recognition of programs. The methodology is extended to completely understand algorithm implementations by providing the information of the program's goal, a specification of programming assignment in tutoring environment. Utilization of goal information is two-fold; extending the role of transformation rules to represent algorithm-specific information and looking for salient graph parts of algorithm plan to determine which has been used to implement the goal. Preliminary evaluation was performed on students' programs containing sort algorithm.     

A planar graph drawing program

This paper describes a program, written in FORTRAN, for a 64K I.C.L. 4130 which will accept data describing the ordering of nodes and branches within the regions of a planar graph, and generate a two-dimensional representation, without crossovers, from these data. The program was written to provide one of the basic ‘tools’ required in the development of a printed wiring board layout program for the electronics industry The program generates display code which is sent to a satellite PDP-7 computer driving a 340 display. On completion of the automatic drawing phase an interactive phase is entered in which the user can ‘tidy’ and label the drawing, by means of keyboard and light-pen commands Brief notes are included on the hardware, the data structures package (MINIJASP, derived from ASP) and the graphics package, employed.     

GraphSET,a tool for simultaneous graph drawing

Problems in simultaneous graph drawing involve the layout of several graphs on a shared vertex set. This paper describes a Graph Simultaneous Embedding Tool, GraphSET, designed to allow the investigation of a wide range of graph embedding problems. GraphSET can be used in the study of several variants of simultaneous embedding including simultaneous geometric embedding, simultaneous embedding with fixed edges, and colored simultaneous embedding with the vertex set partitioned into color classes. The tool has three primary uses: (i) studying theoretical problems in simultaneous graph drawing through the production of examples and counterexamples, (ii) producing layouts of given classes of graphs using built‐in implementations of known algorithms, and (iii) providing a platform for development and implementation of new algorithms and data structures for all variants of simultaneous graph embedding. We also describe the design decisions involved in the construction of GraphSET in terms of the requirements dictated by its applications. GraphSET along with movies illustrating its utility are available at http://graphset.cs.arizona.edu . Copyright © 2010 John Wiley & Sons, Ltd.     

Enhancement of a graph drawing package

An extendable graph drawing package of Fortran subroutines enabling novice programmers to produce a wide variety of charts easily is described. It provides linear, logarithmic and normal probability scales as well as polar graphs. SIMPLEPLOT Mark 2 provides plotting facilities including curve drawing, linear and quadratic regression and the capability for the more experienced programmer to exercise greater control over the appearance of graphs. The design criteria for the package are discussed and a summary of facilities is given.     

权长相合的带权无向图画图算法

针对带权无向图的输出需用边长反映权值大小的问题,提出了一种基于遗传算法的带权无向图画图算法,通过对顶点坐标的编码进行交叉和变异来得到理想的节点坐标,变异算子结合了非一致性变异和单点邻域变异,并在适应度函数中运用顶点平均距离、边交叉数、多度顶点相关边夹角均匀度、边的权值长度比一致程度四个美学标准。实验结果表明,该算法画出的图形连线无交叉,分支清晰,权值—长度相合,能得到清晰、美观且能直观反映权值的可视化输出结果,可应用于带权无向图的可视化输出系统的设计。     

A discriminative graph inferring framework towards weakly supervised image parsing

In this paper, we focus on the task of assigning labels to the over-segmented image patches in a weakly supervised manner, in which the training images contain the labels but do not have the labels’ locations in the images. We propose a unified discriminative graph inferring framework by simultaneously inferring patch labels and learning the patch appearance models. On one hand, graph inferring reasons the patch labels by a graph propagation procedure. The graph is constructed by connecting the nearest neighbors which share the same image label, and multiple correlations among patches and image labels are imposed as constraints to the inferring. On the other hand, for each label, the patches which do not contain the target label are adopted as negative samples to learn the appearance model. In this way, the predicted labels will be more accurate in the propagation. Graph inferring and the learned patch appearance models are finally embedded to complement each other in one unified formulation. Experiments on three public datasets demonstrate the effectiveness of our method in comparison with other baselines.     

A fast successive over-relaxation algorithm for force-directed network graph drawing

Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration sequence used in the algorithm and further, it is hard to estimate the rate of convergence even if the convergence is satisfied. Second, the running time cost is increased intolerablely in drawing largescale graphs, and therefore the advantages of the force-directed approach are limited in practice. This paper is focused on these problems and presents a sufficient condition for ensuring the convergence of iterations. We then develop a practical heuristic algorithm for speeding up the iteration in force-directed approach using a successive over-relaxation (SOR) strategy. The results of computational tests on the several benchmark graph datasets used widely in graph drawing research show that our algorithm can dramatically improve the performance of force-directed approach by decreasing both the number of iterations and running time, and is 1.5 times faster than the latter on average.     

网络图自动绘制的超松弛加速算法

大规模网络的自动布局与绘制问题近年来得到了广泛的研究,其中基于力导引优化的迭代算法成为最成功的方法之一.传统力导引算法在理论与实践中存在两个困难,一是迭代序列收敛性判定及收敛速度估计在理论上尚不完备,二是针对大型网络使用迭代算法的运行时间开销巨大从而极大地限制了其实用价值.本文对这两方面难题进行了探索,首先基于非线性迭代理论给出力导引优化迭代过程收敛速度估计的一种理论方法,其次基于超松弛加速原理给出加速力导引迭代收敛过程的一种实用启发式方法.通过对基准测试数据及应用中的图实例数据进行的实验结果表明,与现有方法相比,本文的超松弛加速方法能有效降低运行时间开销,平均加速达1.5倍左右.本文最后对下一步工作进行了总结和展望.     

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。     

基于语义依存分析的图网络文本分类模型

针对目前已有的文本分类方法未考虑文本内部词之间的语义依存信息而需要大量训练数据的问题,提出基于语义依存分析的图网络文本分类模型TextSGN。首先对文本进行语义依存分析,对语义依存关系图中的节点（单个词）和边（依存关系）进行词嵌入和one-hot编码;在此基础上,为了对语义依存关系进行快速挖掘,提出一个SGN网络块,通过从结构层面定义信息传递的方式来对图中的节点和边进行更新,从而快速地挖掘语义依存信息,使得网络更快地收敛。在多组公开数据集上训练分类模型并进行分类测试,结果表明,TextSGN模型在短文本分类上的准确率达到95.2%,较次优分类法效果提升了3.6%。     

The facial texture analysis for the automatic portrait drawing

It is important to draw the portrait by the facial textures automatically. In order to analyze the detailed textures located at the neighborhood of the eyes, the texture analyzing method is studied. Firstly, we propose the principle of selecting the feature points and the portrait drawing method by B-spline curves using the self-reference parameter. Then, the wavelet transform is used to analyze the position, the direction and the intensity of the double-fold eyelid textures. Experimental results have shown that the facial texture analyzing method is effective for drawing portraits automatically.     

HD-GDD: high dimensional graph dominance drawing approach for reachability query

Efficiently answering reachability queries, which checks whether one vertex can reach another in a directed graph, has been studied extensively during recent years. However, the size of the graph that people are facing and generating nowadays is growing so rapidly that simple algorithms, such as BFS and DFS, are no longer feasible. Although Refined Online Search algorithms can scale to large graphs, they all suffer from the false positive problem. In this paper, we analyze the cause of false positive and propose an efficient High Dimensional coordinate generating method based on Graph Dominance Drawing (HD-GDD) to answer reachability queries in linear or even constant time. We conduct experiments on different graph structures and different graph sizes to fully evaluate the performance and behavior of our proposal. Empirical results demonstrate that our method outperforms state-of-the-art algorithms and can handle extensive graphs.