Independence Numbers of Random Subgraphs of Some Distance Graph

The distance graph G(n, 2, 1) is a graph where vertices are identified with twoelement subsets of {1, 2,..., n}, and two vertices are connected by an edge whenever the corresponding subsets have exactly one common element. A random subgraph G _p (n, 2, 1) in the Erd?os–Rényi model is obtained by selecting each edge of G(n, 2, 1) with probability p independently of other edges. We find a lower bound on the independence number of the random subgraph G_1/2(n, 2, 1).     

On Stability of the Independence Number of a Certain Distance Graph

Problems of Information Transmission - We study the asymptotic behavior of the independence number of a random subgraph of a certain (r, s)-distance graph. We provide upper and lower...     

完全图K97的边染色与4个Ramsey数的新下界

用构造性方法研究完全图K97的边的各种染色,得到4个经典Ramsey数的新下界：R（3,3,8）≥98,R（3,4,6）≥98,R（3,5,5）≥98,R（3,18）≥98。     

On the Expressiveness of Context-Sensitive Graph Grammars

上下文相关图文法是描述可视化语言的形式化工具.为了直观地刻画并高效地分析可视化语言,已有图文法形式框架均着重于文法形式和分析算法的研究,而忽略了对它们之间表达能力的分析.在对已有上下文相关图文法形式框架的关键特征进行分析和归纳的基础上,通过构造不同形式框架之间的转换算法,揭示并形式化证明了它们表达能力之间的关系.而且,转换算法在不同形式框架之间建立了关联,使图文法的应用不必再局限于一个框架,而是可以选择不同框架分别进行图的描述和分析,从而提高了上下文相关图文法的易用性.     

图同构的判定研究

图论中的图同构判定问题仍是一个未能圆满解决的重要问题。文章从图的邻接矩阵的行、列置换出发,得到能加快判定两个图是否同构的一系列性质。在几个性质基础上,提出了一种判定两个图是否同构的搜索算法。接着给出两个实例对该算法加以说明和演示,以便更好地理解这些性质和算法。最后对文章作简要的总结并指出进一步的研究方向。     

On the Parameterized Complexity of Layered Graph Drawing

We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case either the total span or the maximum span of edges can be minimized. In contrast to the Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers. Research initiated at the International Workshop on Fixed Parameter Tractability in Graph Drawing, Bellairs Research Institute of McGill University, Holetown, Barbados, Feb. 9–16, 2001, organized by S. Whitesides. Research of Canada-based authors is supported by NSERC; research of Quebec-based authors is also supported by a grant from FCAR. Research of D.R. Wood completed while visiting McGill University. Research of G. Liotta supported by CNR and MURST.     

On the Representation of Real Numbers Using Regular Languages

Using a lexicographically ordered regular language, we show how to represent an interval of \R . We determine exactly the possible representations of any element in this interval and study the function which maps a representation onto its numerical value. We make explicit the relationship between the convergence of finite words to an infinite word and the convergence of the corresponding approximations to a real number. Received February 13, 2001, and in final form September 21, 2001. Online publication January 14, 2002.     

大规模图处理研究

大数据研究领域的许多问题可以转换为图的问题。本文将阐述鲲鹏大数据系统计算引擎中有关大规模图处理的研究进展以及应用,具体包括高效子图匹配算法、面向图的稀疏数据存储结构和大规模图异步计算模型及其在基因拼接中的应用。     

On Embedding a Graph in the Grid with the Maximum Number of Bends and Other Bad Features

Graph Drawing is (usually) concerned with the production of readable representations of graphs. In this paper, instead of investigating how to produce “good” drawings we tackle the opposite problem of producing “bad” drawings. In particular, we study how to construct orthogonal drawings with many bends along the edges and with large area. Our results show surprising contact points, in Graph Drawing, between the computational cost of niceness and the one of ugliness.     

On Graph Features of Semantic Web Schemas

In this paper, we measure and analyze the graph features of semantic Web (SW) schemas with focus on power-law degree distributions. Our main finding is that the majority of SW schemas with a significant number of properties (respectively, classes) approximate a power law for total-degree (respectively, the number of subsumed classes) distribution. Moreover, our analysis revealed some emerging conceptual modeling practices of SW schema developers: (1) each schema has a few focal classes that have been analyzed in detail (that is, they have numerous properties and subclasses), which are further connected with focal classes defined in other schemas, (2) class subsumption hierarchies are mostly unbalanced (that is, some branches are deep and heavy, while others are shallow and light), (3) most properties have as domain/range classes that are located high at the class subsumption hierarchies, and (4) the number of recursive/multiple properties is significant. The knowledge of these features is essential for guiding synthetic SW schema generation, which is an important step toward benchmarking SW repositories and query language implementations.     

On Certificates and Lookahead in Dynamic Graph Problems

Recent work in dynamic graph algorithms has led to efficient algorithms for dynamic undirected graph problems such as connectivity. However, no efficient deterministic algorithms are known for the dynamic versions of fundamental directed graph problems like strong connectivity and transitive closure, as well as some undirected graph problems such as maximum matchings and cuts. We provide some explanation for this lack of success by presenting quadratic lower bounds on the certificate complexity of the seemingly difficult problems, in contrast to the known linear certificate complexity for the problems which have efficient dynamic algorithms. In many applications of dynamic (di)graph problems, a certain form of lookahead is available. Specifically, we consider the problems of assembly planning in robotics and the maintenance of relations in databases. These give rise to dynamic strong connectivity and dynamic transitive closure problems, respectively. We explain why it is reasonable, and indeed natural and desirable, to assume that lookahead is available in these two applications. Exploiting lookahead to circumvent their inherent complexity, we obtain efficient dynamic algorithms for strong connectivity and transitive closure. Received August 11, 1995; revised August 23, 1996.     

Constructing the Call Graph of a Program

The proliferation of large software systems written in high level programming languages insures the utility of analysis programs which examine interprocedural communications. Often these analysis programs need to reduce the dynamic relations between procedures to a static data representation. This paper presents one such representation, a directed, acyclic graph named the call graph of a program. We delineate the programs representable by an acyclic call graph and present an algorithm for constructing it using the property that its nodes may be linearly ordered. We prove the correctness of the algorithm and discuss the results obtained from an implementation of the algorithm in the PFORT Verifier [1].     

On Dissemination Thresholds in Regular and Irregular Graph Classes

We investigate the natural situation of the dissemination of information on various graph classes starting with a random set of informed vertices called active. Initially active vertices are chosen independently with probability p, and at any stage in the process, a vertex becomes active if the majority of its neighbours are active, and thereafter never changes its state. This process is a particular case of bootstrap percolation. We show that in any cubic graph, with high probability, the information will not spread to all vertices in the graph if p < frac12pp.     

论《图形创意》课程的教育原则

在实施《图形创意》课程的教学过程中,除遵守和贯彻教育学的一般原则外,还要遵守与艺术教育的目的和特点相关联的领悟性原则。本文从形象思维的角度探讨了"知觉促动"(领悟)的原理,并尝试解决《图形创意》课程的学习方法和领悟境界。     

On the Role of the Law of Large Numbers in the Theory of Randomness

Problems of Information Transmission - In the first part of this article, we answer Kolmogorov's question (stated in 1963 in [1]) about exact conditions for the existence of random generators....     

Underflow and the Denormalized Numbers

Although there have been misconceptions about it, gradual underflow fits naturally into the proposed standard and leads to simple, general statements about the arithmetic.