一些新的Hamilton图的必要条件

寻求Hamilton图的适当的特征刻画是图论的一个重大未解决问题，根据图的结构特征，设计了图的顶点的分层方法，研究了Hamilton图中层与层间对外顶点数和对外边数应该满足的关系，分析了Hamilton图中每层顶点数与每层对外项点数的关系，探讨了图与其Hamilton演化图的Hamilton性关系，最后得到一些新的Hamilton图的必要条件。所获得的新的Hamilton图的必要条件实用性强，使用方便，能判断一些原必要条件不能判断的非Hamilton图。     

低度图的最大团求解算法

在图的最大团问题中,当图的顶点数不大于阈值m时,很容易求解其最大团问题,求解算法的时间复杂度为O(d)。给出一种求解低度图的最大团的确定性算法。该算法通过对图按顶点逐步分解实现分别计算,较好地解决低度图的最大团问题。算法时间复杂度为O(d•n3)。其中,n表示图的顶点数,图中顶点的最大度小于m或者图可以通过逐个删除度小于m的顶点而使所有顶点的度都小于m。     

强竞赛图的强连通性

D=(V,A)为一个有向图,其中,V为顶点集,A为弧集,A中的元素是有序对(u,v),称为弧。设u和v是有向图D的两个顶点,若从u到v存在一条有向路,则称顶点v是从u可达的,或称从u可达v。若有向图D中任何两个顶点是互相可达的,则称D为强连通图。若有向图T中任意两个顶点之间恰有一条弧,则称T为竞赛图。一个强连通的竞赛图T称为强竞赛图。论文研究顶点个数大于的强竞赛图T的性质,并利用该性质给出了Moon定理的另外一种证明。     

一种基于核心顶点的无参图聚类算法

针对许多经典的图聚类算法存在输入参数难以确定、时间复杂度过高、聚类精度较低等缺点,本文提出了一种无需输入参数的基于核心顶点的图聚类算法（NGCC）。该算法将相似的顶点分配到同一个簇后,再利用PageRank算法发现核心顶点以形成初始簇。然后,将剩余的未标记顶点进行分配,形成最终簇结构。实验结果证明,NGCC算法在无需任何参数的条件下,在不同规模的数据集上的聚类质量与对比的经典图聚类算法相当或更优,而且适用范围更广。     

Connectedness strength of two vertices in an uncertain graph

In practical applications of graph theory, due to some reasons, different types of uncertainties are frequently encountered. In this paper, we employ uncertainty theory to investigate an uncertain graph in which complete determination of whether two vertices are joined by an edge or not cannot be carried out. By means of uncertainty theory, the concepts of connectedness strength of two vertices in an uncertain graph and strength of an uncertain path are proposed. A method to calculate the connectedness strength of two vertices is also described. After that, we investigate the relationship between the connectedness strength of two vertices and the connectedness index of the uncertain graph. This relationship provides a new method to obtain the connectedness index of an uncertain graph.     

Longest (s,t)-paths in L-shaped grid graphs

The longest path problem, that is, finding a simple path with the maximum number of vertices, is a well-known NP-hard problem with many applications. However, for some classes of graphs, including solid grid graphs and grid graphs with some holes, it is open. An L-shaped grid graph is a special kind of a rectangular grid graph with a rectangular hole. In this paper, we show that a longest path between two given vertices s and t of an L-shaped grid graph can be computed in linear time.     

基于Spark的并行社区发现算法

针对大规模图数据顶点聚类进行研究,提出了一种基于Spark的并行社区发现算法,其在基于极值优化的串行社区发现算法的基础上设计而成。此外还针对该串行算法在簇调整时因选择顶点数量过少而影响算法运行效率的问题,提出了一种多个顶点选择方法。该方法会计算一个阈值并发现所有适应度值小于该阈值的顶点,作为被选择的顶点;由于阈值是基于所有顶点的适应度值计算出来的,为了避免非常大的适应度值对阈值造成的影响该方法会限制被选择顶点的数量,若被选择的顶点过多,算法只保留其中的一部分。同时,还提出了一种顶点过滤方法,其可以有效减少图数据的数据量。在实验当中,提出算法的运行时间明显短于比较的其他基于Spark的并行化社区发现算法,可以发现提出算法的运行速度相对较快。     

特殊图的图修正问题研究综述

图修正问题是指在一个图中进行删除点、删除边或加边操作,使这个图转变成另一个具有某种特殊性质的图。图修正问题一直被广泛研究,尤其对弦图、区间图以及单位区间图的图修正问题的研究更是如此。弦图是完美图中最重要的一类图,也是(单位)区间图的父类图,很多经典的NP难问题在弦图上都是多项式可解的。区间图以及单位区间图在生物计算上有着广泛的应用。对这几类图的图修正问题的研究对计算机理论和实践有很大的贡献。首先介绍并总结了关于弦图、区间图以及单位区间图的图修正问题的重要算法和技术,然后对这些问题的研究现状进行分析,并提出了今后研究中值得关注的问题。     

一种基于元胞自动机的无向图剖分优化算法

运用元胞自动机理论,针对无向图剖分优化问题进行了分析和建模,提出了一种元胞自动机模型以及基于该模型的无向图剖分优化算法。在该元胞自动机模型中,元胞对应于无向图中的结点,元胞的邻居对应于邻接结点,元胞空间对应于无向图中的结点集,元胞的状态对应于所在的结点子集。实验及分析表明该算法不仅能找到无向图的近似最优剖分,而且有效地降低了空间复杂度和时间复杂度。     

Embedding a triangular graph within a given boundary

Given a 3-vertex-connected triangular planar graph and an embedding of its boundary vertices, can the interior vertices be embedded to form a valid triangulation? We describe an algorithm which decides this problem and produces such an embedding if it exists.     

ExPregel: a new computational model for large‐scale graph processing

These days, large‐scale graph processing becomes more and more important. Pregel, inspired by Bulk Synchronous Parallel, is one of the highly used systems to process large‐scale graph problems. In Pregel, each vertex executes a function and waits for a superstep to communicate its data to other vertices. Superstep is a very time‐consuming operation, used by Pregel, to synchronize distributed computations in a cluster of computers. However, it may become a bottleneck when the number of communications increases in a graph with million vertices. Superstep works like a barrier in Pregel that increases the side effect of skew problem in distributed computing environment. ExPregel is a Pregel‐like model that is designed to reduce the number of communication messages between two vertices resided on two different computational nodes. We have proven that ExPregel reduces the number of exchanged messages as well as the number of supersteps for all graph topologies. Enhancing parallelism in our new computational model is another important feature that manifolds the speed of graph analysis programs. More interestingly, ExPregel uses the same model of programming as Pregel. Our experiments on large‐scale real‐world graphs show that ExPregel can reduce network traffic as well as number of supersteps from 45% to 96%. Runtime speed up in the proposed model varies from 1.2× to 30×. Copyright © 2015 John Wiley & Sons, Ltd.     

一种基于图割的改进立体匹配算法

针对基于图割法的立体匹配算法耗时太长的问题,提出了一种基于简化网格图的立体匹配算法．算法 通过区域匹配算法得到每个像素的初始视差值,然后只保留完整网格图的部分可能的视差值,去除其余大部分的节 点和边缘,建立简化的网格图．该方法大大缩减了网格图的容量,缩短匹配所用时间,并且能够选用更大的视差范 围．实验证明,该算法能够得到比较理想的视差图,而且大大缩短立体匹配所用时间．     

Linear-Time Recognition of Circular-Arc Graphs

A graph G is a circular-arc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a linear-time algorithm for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs that realize it.     

A simple algorithm to find Hamiltonian cycles in proper interval graphs

We present an algorithm to find a Hamiltonian cycle in a proper interval graph in O(m+n) time, where m is the number of edges and n is the number of vertices in the graph. The algorithm is simpler and shorter than previous algorithms for the problem.     

知识图谱划分算法研究综述

知识图谱是人工智能的重要基石,因其包含丰富的图结构和属性信息而受到广泛关注.知识图谱可以精确语义描述现实世界中的各种实体及其联系,其中顶点表示实体,边表示实体间的联系.知识图谱划分是大规模知识图谱分布式处理的首要工作,对知识图谱分布式存储、查询、推理和挖掘起基础支撑作用.随着知识图谱数据规模及分布式处理需求的不断增长,如何对其进行划分已成为目前知识图谱研究的热点问题.从知识图谱和图划分的定义出发,系统性地介绍当前知识图谱数据划分的各类算法,包括基本、多级、流式、分布式和其他类型图划分算法.首先,介绍4种基本图划分算法:谱划分算法、几何划分算法、分支定界算法、KL及其衍生算法,这类算法通常用于小规模图数据或作为其他划分算法的一部分;然后,介绍多级图划分算法,这类算法对图粗糙化后进行划分再投射回原始图,根据粗糙化过程分为基于匹配的算法和基于聚合的算法;其次,描述3种流式图划分算法,这类算法将顶点或边加载为序列后进行划分,包括Hash算法、贪心算法、Fennel算法,以及这3种算法的衍生算法;再次,介绍以KaPPa、JA-BE-JA和轻量级重划分为代表的分布式图划分算法及它们的衍生算法;同时,在其他类型图划分算法中,介绍近年来新兴的2种图划分算法:标签传播算法和基于查询负载的算法.通过在合成与真实知识图谱数据集上的丰富实验,比较了5类知识图谱代表性划分算法在划分效果、查询处理与图数据挖掘方面的性能差异,分析实验结果并推广到推理层面,获得了基于实验的知识图谱划分算法性能评价结论.最后,在对已有方法分析和比较的基础上,总结目前知识图谱数据划分面临的主要挑战,提出相应的研究问题,并展望未来的研究方向.     

Efficient parallel algorithms for breadth first spanning forests of general graphs

Ghosh and Bhattacharjee propose [2] (Intern. J. Computer Math., 1984, Vol. 15, pp. 255-268) an algorithm of determining breadth first spanning trees for graphs, which requires that the input graphs contain some vertices, from which every other vertex in the input graph can be reached. These vertices are called starting vertices. The complexity of the GB algorithm is O(log² n) using O{n ³) processors. In this paper an algorithm, named BREADTH, also computing breadth first spanning trees, is proposed. The complexity is O(log² n) using O{n ³/logn) processors. Then an efficient parallel algorithm, named- BREADTHFOREST, is proposed, which generalizes algorithm BREADTH. The output of applying BREADTHFOREST to a general graph, which may not contain any starting vertices, is a breadth first spanning forest of the input graph. The complexity of BREADTHFOREST is the same as BREADTH.     

A Coloring Problem With Restrictions of Adjacent Colors

The coloring problem is a well-known problem of graphs. This paper considers a new coloring problem with restrictions such that some pairs of colors cannot be used for adjacent vertices, called coloring problem with restrictions of adjacent colors . The restriction of adjacent colors can be represented by a graph H called a restriction graph , i.e., each vertex represents a color and each edge means that the two colors corresponding to the two end-vertices of the edge cannot be used for adjacent vertices. This paper shows some properties of the new coloring problem. It also presents a necessary and sufficient condition such that a restriction graph H cannot be replaced with a more simple graph, when H is a cactus with no 3-cycle.     

Matching preclusion and conditional matching preclusion for pancake and burnt pancake graphs

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion destroys all perfect matchings in the graph. The optimal matching preclusion sets are often precisely those which are induced by a single vertex of minimum degree. To look for obstruction sets beyond these, the conditional matching preclusion number was introduced, which is defined similarly with the additional restriction that the resulting graph has no isolated vertices. In this paper we find the matching preclusion and conditional matching preclusion numbers and classify all optimal sets for the pancake graphs and burnt pancake graphs.     

用多层次聚类法完成的大规模关系图的可视化

提出了一种新的大规模图形可视化技术.它可显示含有几万个接点和边的大规模关系图.为了完成对图形的抽象化。一个多层次的聚类图形从原始的大规模关系图中抽取了出来.这种抽取是建立在大规模关系图的内在结构基础上来完成的.一种递规封入式的几何划分算法被应用来完成对几何空间的优化,在具体的制图技术上,使用了一种用力导向布局算法和环形制图法相结合的新方法,从而完成了对显示空间的优化和美擘上的优化.同时也讨论了相关的人机交互技术,所采用的人机交互算法不仅能让使用者从上到下层次式地浏览整个聚类图形。同时也能提供多层次聚类图形的并行浏览.动画技术也同时被运用,以保护使用者的精神图不被打乱.     

基于谱方法的无向赋权图剖分算法*

在多水平方法初始剖分阶段提出了一种基于谱方法的无向赋权图剖分算法SPWUG,给出了基于Lanczos迭代计算Laplacian矩阵次小特征值及特征向量的实现细节。SPWUG算法借助Laplacian矩阵次小特征值对应的特征向量,刻画了节点间相对距离,将基于非赋权无向图的Laplacian谱理论在图的剖分应用方面扩展到无向赋权图上,实现了对最小图的初始剖分。基于ISPD98电路测试基准的实验表明,SPWUG算法取得了一定性能的改进。实验分析反映了在多水平方法中,最小图上的全局近似最优剖分可能是初始图的局部最