一个求解层次图边交叉数最小化问题的遗传算法

最小化边交叉数是层次图绘制过程中的一个关键步骤,直接影响着层次图的可读性。提出了一个基于 遗传算法的层次图边交叉数最小化算法,详细地给出了编码表示方法以及遗传算子的设计。与常用的启发算法 相比,该算法得到了更好的计算结果,此外算法简单且易于实现。     

—个求解层次图边交叉数最小化问题的遗传算法

最小化边交叉数是层次图绘制过程中的一个关键步骤，直接影响着层次图的可读性。提出了一个基于遗传算法的层次图边交叉数最小化算法，详细地给出了编码表示方法以及遗传算子的设计。与常用的启发算法相比，该算法得到了更好的计算结果，此外算法简单且易于实现。     

基于结点间距离统计的无向无权图同构判别

按照同构图的定义判断两个图是否同构,最坏情况下其时间复杂度是O(N!),当结点数N比较大时,计算速度非常慢,针对该问题,提出一种通过统计结点间距离和按照距离分层,计算同层结点间的关联边数以及关联结点数来研究图中各结点差异的算法,该算法可以给出两个图的结点间可能的对应关系.如果两个图的结点距离数组及对应结点的层结点关联数组不能一一对应,其时间复杂度仅为O(N4),否则,根据结点间可能的对应关系,避免遍历所有结点序号的交换,计算量可以成倍地下降.     

基于代数连通性的复杂网络割边模型研究

传统的GN算法每次迭代删除一条边,时间复杂度高,其变种时间复杂度有所下降,但分割精度也有待于提高;在复杂网络图中,图的连通性是由拉普拉斯矩阵的第二小特征值决定的,通过最小化网络连通性,提出了贪婪谱优化割边模型,该模型在GN算法基础上,一次删除多条边,为避免出现边过度分割,每条边设置了权重;为了进一步降低时间复杂度,选择网络代数连通性下降最快的边进行删除,提出了基于边中心性测度的割边模型,与传统的利用最短距离和随机游走不同,模型采取谱分析方法对每条边定义边中心性测度,速度更快,分割精度能到达要求,适合处理中规模社区结构。     

基于遗传算法的概念格布局优化

针对概念格布局过程中产生的边交叉数过多问题,分析了求解概念格图形中边交叉数问题的方法,并结合遗传算法,提出了减少边交叉数的优化策略,通过目标函数计算出概念格层次图的边交叉数最少时格节点的布局序列,从而达到在二维概念格图形布局过程中尽量减少边交叉数的目的。     

一种基于继承次序与相关度的布图算法

在层次图边交叉最小化问题上,常规启发算法或者时间复杂度大或者布图效果不佳。基于Sugiyama布图算法模式,提出了一种交叉数减少算法,并从布局与布线两个主要方面介绍了其实现过程。两层图上的实验表明,该算法具有较好的性能,一定程度上克服了时间复杂度与效果的矛盾。     

一种基于分层图的改进SPFA算法

针对数据结构课程教学中顶点数受限的最短路径问题,提出一种基于图分层的改进SPFA算法——K_SPFA。借鉴图分层思想,将原图拓展为层数与顶点限制数相等的图层,将原图中的边拓展成图层间的边。利用2个同步循环的FIFO队列和贪心策略,对SPFA算法的数据存储结构和最短路径更新操作进行改进,从而实现原图中顶点数受限的最短路径寻找。实验结果表明,K_SPFA具有较低的平均时间复杂度。     

基于分层法的通风网络图绘制算法研究

最长路径法绘制通风网络图需要频繁地搜索任意两个节点之间的最长路径,采用深度优先搜索导致大量的时间浪费在无用路径的搜索过程中;且采用几何相交方法判断分支交叉,效率低且无法有效地减少分支交叉数。提出了将分层法引入到通风网络图绘制中。采用最长路径法对网络图进行节点分层,求解整数规划问题优化节点分层减少长边;采用模拟退火遗传算法优化节点排序,从拓扑上减少分支交叉数。为了减少无意义地搜索最长路径过程,采用最长路径并联通路法计算节点坐标和分支形状。给出了基于分层法的通风网络图绘制的测试例子。     

大图结构特征对划分效果的影响

针对大图结构特征如何影响划分效果这一问题,提出一种通过顶点度分布特征来描述大图结构特征的方法。首先,基于真实的图数据产生若干顶点数和边数相同、但结构特征不同的仿真数据集,通过实验计算真实图与仿真图之间的相似度,证明该方法对描述真实大图结构特征的有效性。然后,通过Hash和点对交换划分算法,验证图结构特征与划分效果之间的关系。当点对交换划分算法执行到5万次时,划分一个有6301个顶点和20777条边的真实图其交叉边数比Hash划分算法降低了54.32%,划分仿真图数据集中结构特征差异明显的两个图时,交叉边数分别为6233和316。实验结果表明,点对交换划分算法能够减少交叉边数,图的顶点度分布差异越大,划分后交叉边数越少,划分效果越好,因此大图结构特征影响其划分效果,这为建立图的结构特征与划分效果之间的关系模型研究奠定了基础。     

一种新的概念格图形布局优化策略

层与层之问边交叉数的多少在概念格层次图布局中尤为重要,它直接影响概念格的可读性和可理解性.如何既能实现人机交互方便操作,又能有效地减少边的交叉数,已成为目前概念格图形布局研究中的主要问题.分析了概述格布局的国内外发展现状,介绍了如何求解概念格图形中层与层之间边交叉数问题的方法,然后结合遗传算法,提出了一种新的在概念格图形布局过程中减少边交叉数问题的优化策略,有效地减少了二维概念格图形布局过程中边的交叉.     

Inserting an Edge into a Planar Graph

Computing a crossing minimum drawing of a given planar graph G augmented by an additional edge e where all crossings involve e, has been a long standing open problem in graph drawing. Alternatively, the problem can be stated as finding a combinatorial embedding of a planar graph G where the given edge e can be inserted with the minimum number of crossings. Many problems concerned with the optimization over the set of all combinatorial embeddings of a planar graph turned out to be NP-hard. Surprisingly, we found a conceptually simple linear time algorithm based on SPQR-trees, that is able to find a solution with the minimum number of crossings.     

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。     

ImPrEd: An Improved Force‐Directed Algorithm that Prevents Nodes from Crossing Edges

PrEd [ [Ber00] ] is a force‐directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts of planar graph drawing algorithms, interacting with a graph layout, and drawing Euler‐like diagrams. The algorithm ensures that nodes do not cross edges during its execution. However, PrEd can be computationally expensive and overly‐restrictive in terms of node movement. In this paper, we introduce ImPrEd: an improved version of PrEd that overcomes some of its limitations and widens its range of applicability. ImPrEd also adds features such as flexible or crossable edges, allowing for greater control over the output. Flexible edges, in particular, can improve the distribution of graph elements and the angular resolution of the input graph. They can also be used to generate Euler diagrams with smooth boundaries. As flexible edges increase data set size, we experience an execution/drawing quality trade off. However, when flexible edges are not used, ImPrEdproves to be consistently faster than PrEd.     

Crossing Minimization for Symmetries

We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NP-hard, even if the order of orbits around the rotation center or along the reflection axis is fixed. We devise an O(m log m) algorithm for computing a crossing minimal drawing if inter-orbit edges may not cross orbits, showing in particular that intra-orbit edges do not contribute to the NP-hardness of the crossing minimization problem for symmetries.     

Drawing complete binary trees inside rectilinear polygons

Most of graph drawing algorithms draw graphs on unbounded planes. However, there are applications that require graphs to be drawn on the plane inside a given polygon. In this paper, a new algorithm for planar orthogonal drawing of complete binary trees inside rectilinear polygons is presented. Uniform distribution of nodes of graphs on drawing regions is one of the aesthetics criteria in graph drawing. The goal of this paper is to produce planar orthogonal drawings with a relatively uniform node distribution and few edge bends. The proposed algorithm can be considered as a generalization of the H-tree layout method for rectilinear polygons. A new linear time algorithm is also given for bisecting rectilinear polygons into two equi-area rectilinear sub-polygons.     

Drawing layered graphs with port constraints

Complex software systems are often modeled using data flow diagrams, in which nodes are connected to each other through dedicated connection points called ports. The influence a layout algorithm has on the placement of ports is determined by port constraints defined on the corresponding node.In this paper we present approaches for integrating port constraints into the layer-based approach to graph drawing pioneered by Sugiyama et al. We show how our layout algorithm, called KLay Layered, progresses from relaxed to more restricted port constraint levels as it executes, and how established algorithms for crossing minimization and edge routing can be extended to support port constraints. Compared to the previous layout algorithms supporting ports, our algorithm produces fewer edge crossings and bends and yields pleasing results.We also explain and evaluate how layout algorithms can be kept simple by using the concept of intermediate processors to structure them in a modular way. A case study integrating our layout algorithm into UC Berkeley's Ptolemy tool illustrates how KLay Layered can be integrated into Java-based applications.     

Drawing graphs with right angle crossings

Cognitive experiments show that humans can read graph drawings in which all edge crossings are at right angles equally well as they can read planar drawings; they also show that the readability of a drawing is heavily affected by the number of bends along the edges. A graph visualization whose edges can only cross perpendicularly is called a RAC (Right Angle Crossing) drawing. This paper initiates the study of combinatorial and algorithmic questions related to the problem of computing RAC drawings with few bends per edge. Namely, we study the interplay between number of bends per edge and total number of edges in RAC drawings. We establish upper and lower bounds on these quantities by considering two classical graph drawing scenarios: The one where the algorithm can choose the combinatorial embedding of the input graph and the one where this embedding is fixed.     

半边图与挤出吸入算法及制造单元设计

提出半边自组图理论,半边附属于顶点,一对半边可结合为边。用半边图来描述复杂组合优化问题的可能解,在此基础上设计了针对图的挤出吸入算法,用此算法求解了一个典型的复杂组合优化问题,制造单元设计问题。示例表明,半边图语言能够准确地表达可能解中的复杂结构和各种约束,20台机器50种零件分组实验证明,4次迭代计算即可达到优化目标。     

一种基于T-Snake模型的医学图像分割方法

改进的T-Snake算法首先在分水岭法中,对相邻区域以其像素数、灰度均值和灰度方差定义距离,并据其在图像上建立新的连通图,以对图像过度分割而产生的一些过小区域合并;其次,在模型跨边缘时,利用已分割断层图像中模型内部区域的统计特征,用区域生长法获取内点并重新参数化模型,使模型不再跨边缘,以保证模型形变到正确的边缘。算法在MATLAB上验证通过。