新型电路版图布局布线算法设计

调研了电路自动布局布线技术的国内外研究现状,在此基础上设计了一种面向中等规模电路布局布线算法,主要用于大型版图设计软件的模块测试环节,为用户提供各模块初步的布线布局结果,方便用户高效查找并修正错误点,填补了我国在相关领域的空白.建立了超图模型并转换为图模型,改进了Stoer-Wagner算法并利用该算法和Fiduccia-Mattheyses算法对图进行了基于最小割理论的划分,从而构建出一棵划分树.在这棵树的基础上设计了一种二元相对移动算法来确定各个电路元件的位置,大大降低了布局拥挤度,提高了美观度,对于数百元件的电路均能在0.5s内得出布局结果.基于A*算法在多个方面做了改进,提高了布线速度,对于线路数1000以下的元件能在0.1 s～60 s内得出结果,实现了100％ 布通率以及均匀的布局布线效果.     

求解布局模型的并行矩阵算法研究

布局设计通常要建立抽象状态空间模型。求解布局模型，实现从模型状态到坐标图的转化，是计算机辅助布局设计的重要研究内容之一。本文在简要介绍一种层次布局模型ＨＬＭ１的基础上，引入了模型的解的概念；研究了ＨＬＭ１的子模型－层次约束图解的存在条件；提出了求解层次约束图，实现从模型到坐标图转化以及检测约束矛盾的一种并行矩阵算法，并给出了一个计算实例。     

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     

Un metodo per la determinazione di un albero con lati pre-assegnati o meno in un grafo non-orientato descritto mediante la matrice di adiacenza

A computer oriented algorithm is given for the determination of a tree in a nondirected linear graph described by its adjacency matrix. The algorith allows two types of constraints for the tree to be found; it can be requested: 1. to involve some given edges. 2. not to involve some other given edges. The computation speed can be improved, when a centre of the graph is nown; an optimization of the procedure is given for this case. The storage requirement is pratically reduced to the only required by the adjacency matrix.     

Constrained Graph Layout

Most current graph layout technology does not lend itself to interactive applications such as animation or advanced user interfaces. We introduce the constrained graph layout model which is better suited for interactive applications. In this model, input to the layout module includes suggested positions for nodes and constraints over the node positions in the graph to be laid out. We describe four implementations of layout modules which are based on the constrained graph layout model. The first three implementations are for undirected graph layout while the fourth is for tree layout. The implementations use active set techniques to solve the layout. Our empirical evaluation shows that they are quite fast and give reasonable layout.     

三角网格模型的基本群分割

提出一种有效的三角网格模型分割方法。用Dijkstra算法求出三角网格模型上任意给定一个基点到其余顶点的最短路径树;求出该模型对偶图的最大生成树,且对偶图的边与该最短路径树的边不相交;找出该模型上所有既不属于最短路径树也不和最大生成树相交的边,这些边分别与最短路径树组成的最短环集合就是给定基点处的基本群,沿着这些最短环就可以把网格分割成一个拓扑同胚于圆盘的区域。实验结果表明,该分割方法可以快速、有效地实现网格的分割。     

铁路信号站场图形一致性检测的算法设计

分析了铁路信号计算机联锁系统中的站场拓扑图形生成机理问题,阐述了图形设备单元的设计过程及其与道岔、信号机及区段数据基的实时对应关系;提出了图形绘制更新流程和图形一致性检测程序流程,对绘图类与联锁程序和通信接口的关系进行了表述,并给出了一种基于代价有向站场拓扑图的k步扩散进路搜索算法;通过C++编程实现了上述图形检测生成算法,并在工程项目中进行了应用,最后对具体的实例进行了算法仿真模拟。     

Visual exploration of complex time-varying graphs

Quasi-trees, namely graphs with tree-like structure, appear in many application domains, including bioinformatics and computer networks. Our new SPF approach exploits the structure of these graphs with a two-level approach to drawing, where the graph is decomposed into a tree of biconnected components. The low-level biconnected components are drawn with a force-directed approach that uses a spanning tree skeleton as a starting point for the layout. The higher-level structure of the graph is a true tree with meta-nodes of variable size that contain each biconnected component. That tree is drawn with a new area-aware variant of a tree drawing algorithm that handles high-degree nodes gracefully, at the cost of allowing edge-node overlaps. SPF performs an order of magnitude faster than the best previous approaches, while producing drawings of commensurate or improved quality     

Flow equivalent trees in undirected node-edge-capacitated planar graphs

Given an edge-capacitated undirected graph G=(V,E,C) with edge capacity , n=|V|, an s−t edge cut C of G is a minimal subset of edges whose removal from G will separate s from t in the resulting graph, and the capacity sum of the edges in C is the cut value of C. A minimum s−t edge cut is an s−t edge cut with the minimum cut value among all s−t edge cuts. A theorem given by Gomory and Hu states that there are only n−1 distinct values among the n(n−1)/2 minimum edge cuts in an edge-capacitated undirected graph G, and these distinct cuts can be compactly represented by a tree with the same node set as G, which is referred to the flow equivalent tree. In this paper we generalize their result to the node-edge cuts in a node-edge-capacitated undirected planar graph. We show that there is a flow equivalent tree for node-edge-capacitated undirected planar graphs, which represents the minimum node-edge cut for any pair of nodes in the graph through a novel transformation.     

面向关键字流图的相似程序间测试用例的重用

软件测试是软件开发中重要的一环,能有效地提高软件的可靠性和质量.而测试用例的重用可减少软件测试的工作量,提升测试的效率.提出一种面向关键字流图的相似程序间测试用例的重用方法,该方法将程序已经生成的测试数据重用到与之相似的程序中.可见,探究测试用例重用的前期工作是判定程序的相似性.对于程序相似性的判定,给出根据关键字流图相似性比较的方法：首先,将程序代码中的关键字存储在流图所对应的节点中,构建关键字流图;接下来,利用动态规划算法查找待测程序关键字流图的最大公共子图;最后,根据最大公共子图距离算法计算程序的相似度.较高相似程度的程序可用到测试用例重用的方法中.在利用遗传算法生成测试用例时,引用相似程序中适应度较高的测试用例,使种群在进行进化操作过程中不断与这些用例进行交叉,加快用例的生成效率.实验表明：将测试用例重用在相似程序的测试生成中,与传统方法相比,在覆盖率和平均进化代数等方面均有明显优势.     

Optimal design of flat patterns for 3D folded structures by unfolding with topological validation

There are applications in the sheet metal, paperboard, packaging and various other industries for the computer-aided design of flat patterns for folding into some desired 3D folded structure made of piecewise flat faces. This paper describes a methodology for the automatic development of flat patterns for any given folded structure based on enumerating all possible spanning trees of the face adjacency graph (the graph that represents the connectivity among the faces of the structure) since any spanning tree represents a potential topological unfolding of that structure. Complications found in non-manifold structures, such as where more than two faces are joined at one common edge, are also addressed in this work by way of recognizing topologically invalid spanning trees. Furthermore, a strategy is also developed to detect overlapping of faces within the pattern purely by checking its topology defined in the spanning tree, without first having to geometrically construct the pattern layout. Finally, three measures of compactness are adopted as the optimality criteria for the methodology to output flat pattern results ranked according to their compactness. The procedure is implemented as a computer program and applied to six example structures in this paper to illustrate the capabilities of the methodology.     

基于DOM树和递归X—Y分割算法的Zone树模型

在分析DOM树的基础上提出一种基于DOM树和递归X—Y分割算法,可以根据网页的几何布局生成Zone树模型。描述了将Zone树模型和递归X—Y算法应用到文献数据检索的优越性,给出构建Zone树模型的算法。该模型主要用于在线文献的数据提取,具有速度快、准确性高等特点,优于目前大多数浏览器所采用的DOM树结构。     

一种用于Marching-Graph图形绘制的快速收敛布局算法

Marching-Graph是一种将图形隐喻技术和空间隐喻技术集成为一体的新的可视化方法.它为用户提供了高度可交互性地图,使用户可访问那些具有地理属性的信息的逻辑结构.它通过有效的人图交互和跨空间浏览为用户提供了一种可视分析和挖掘未知信息的机制,而不是将已知的信息呈现在地图上.然而,传统的力导向布局算法在达到力量均衡配置方面非常慢.为使一个图形布局收敛,它们通常需花费几十秒的时间.因此。当用户快速行进于地理区间时,那些力导向布局算法就不能满足快速绘制一系列图形的要求.提出了一种快速收敛布局方法,当用户在Marching-Graph中通过力导向布局逐步探究一系列图形时,它可以加速交互时间.通过结合辐射树绘图技术和力导向图形绘制方法来取得能量最小化的快速收敛.     

基于图论的路网交通检测器之布点

为获取各路段的交通流量,将路网检测器布点问题转变成寻求有向图的流控制子图的问题.首先将任意路网抽象为有向图,定义弧的度表征路段的重要性,证明完全有向回路图(CCG)的若干结论后给出CCG最小流控制子图的获取算法,同时给出有向图非回路部分的流控制子图获取方法,进而提出能在任意路网上进行检测器优化布点的完整算法.算例选取广州火车东站附近的路网,结果验证了所提出的方法的有效性.     

基于主干子图的幂律特征图聚类算法

从Internet拓扑的幂律特征（度分布律）出发,定义了主干子图的相关概念,证明了主干子图的若干性质,并在此基础上给出了基于主干子图的聚类算法。该算法可应用于有幂律特征的大型图的混合布局,也可为幂律特征网络的研究提供参考。幂律特征图可以被分解为一个主干子图和多个子树。主干子图是一些度相对较高节点的集合;而子树则正好相反,幂律特征有效地保证了节点度分布的非均一特性。基于主干子图理论的图聚类算法可以分成两个步骤,即主干子图生成算法和桩树生成算法。主干子图Gs(Vs,Es)与原始图G(V,E)之间的同态等价关系     

基于最小割集的安全性测试用例的动态生成

利用故障树的原理和方法,对基于故障树最小割集的安全性测试用例动态生成进行了研究.首先阐述了故障树和故障树最小割集的概念及数学描述,然后给出了故障树最小割集的生成算法,最后在此基础上提出了基于故障树最小割集的动态生成安全性测试用例的算法.     

A Flexible Algorithm for Generating All the Spanning Trees in Undirected Graphs

In this paper we propose an algorithm for generating all the spanning trees in undirected graphs. The algorithm requires O (n+m+ τ n) time where the given graph has n vertices, m edges, and τ spanning trees. For outputting all the spanning trees explicitly, this time complexity is optimal. Our algorithm follows a special rooted tree structure on the skeleton graph of the spanning tree polytope. The rule by which the rooted tree structure is traversed is irrelevant to the time complexity. In this sense, our algorithm is flexible. If we employ the depth-first search rule, we can save the memory requirement to O (n+m). A breadth-first implementation requires as much as O (m+ τ n) space, but when a parallel computer is available, this might have an advantage. When a given graph is weighted, the best-first search rule provides a ranking algorithm for the minimum spanning tree problem. The ranking algorithm requires O (n+ m + τ n) time and O (m+ τ n) space when we have a minimum spanning tree. Received January 21, 1995; revised February 19, 1996.     

An optimal graph theoretic approach to data clustering: theory andits application to image segmentation

A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph 𝒢 with arc capacities assigned to reflect the similarity between the linked vertices. Clustering is achieved by removing arcs of 𝒢 to form mutually exclusive subgraphs such that the largest inter-subgraph maximum flow is minimized. For graphs of moderate size (~ 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of 𝒢, which can be efficiently constructed using the Gomory-Hu algorithm (1961). However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices. The new clustering algorithm is applied to the image segmentation problem. The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to minimum cuts in 𝒢), which consist mostly of strong edges, while rejecting contours containing isolated strong edges. This method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours     

图神经网络下的生成式室内家具摆放

自动的室内家具摆放在家居设计、动态场景生成等应用中具有显著的意义.传统算法往往通过显式的空间、语义和功能性上物体之间的关系来理解场景的内部结构,并进一步辅助室内场景的生成.随着大规模室内场景数据集的出现,提出将零散的输入家具编码进图结构,并利用图神经网络中迭代的消息传递隐式地学习场景的分布先验.为了满足家具摆放的多样性...