The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

The Number of Maximal Independent Sets in Quasi-Tree Graphs and Quasi-Forest Graphs

A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set V(G) is called a quasi-tree graph (respectively, quasi-forest graph), if there exists a vertex x ∈V(G) such that G −x?is a tree (respectively, forest). In this paper, we survey on the large numbers of maximal independent sets among all trees, forests, quasi-trees and quasi-forests. In addition, we further look into the problem of determining the third largest number of maximal independent sets among all quasi-trees and quasi-forests. Extremal graphs achieving these values are also given.

Minimum Dominating Tree Problem for Graphs

A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.

The Rupture Degree of Graphs with k-Tree

A k-tree of a connected graph G is a spanning tree with maximum degree at most k. The rupture degree for a connected graph G is defined by , where and , respectively, denote the order of the largest component and number of components in . In this paper, we show that for a connected graph G, if for any cut-set , then G has a k-tree.

The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks

In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

PATHS BETWEEN TWO VERTICES IN A TREE GRAPH

Let T(G)be the tree graph of a simple graph G.It is proved that ifT and T′are two vertices of T(G)such that d_T(G)(T)(?)d_T(G}(T′),then there ared_T(G)(T) internally disjoint paths in T(G) joining T and T′.

Uniquely Tree Colorable Graphs

In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.

MINIMUM CONGESTION SPANNING TREES IN BIPARTITE AND RANDOM GRAPHS

The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.

Clique-transversal number of graphs whose clique-graphs are trees

Given a graph G, a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and ｜C｜ ≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as τC（G）, is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K（G）, is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F = {G｜ K（G） is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus τC（G）/｜G｜ ≤ 1/2 for all G ∈F.

An Optimal Parallel Algorithm for Constructing a Spanning Tree on Proper Circle Trapezoid Graphs

Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.

案例索引BCS-Tree及其构建方法研究

为克服现有案例索引方法存在的不足,提出了一种新的索引结构BCS-Tree.首先,对松弛聚类(graph-based relaxed clustering,GRC)算法进行了自适应改进,以克服现有基于聚类方法受初值影响大、只能适应凸形聚类等缺点;其次,将KICA与最小外接矩阵(minimum bounding rectangle,MBR)结合,增强了MBR方法对非线性和非正态分布数据的处理能力;然后,在给出双基点选择方法的基础上,提出了基于改进GRC和双基点聚类分割的BCS-Tree构建方法;最后,基于对查询点和案例数据之间可能分布关系的全面分析,设计了BCS-Tree的查询算法,并结合理论推导和实例验证,对BCS-Tree及其查询算法进行了分析.结果证明,所提的索引构建方法具有较强的参数鲁棒性和适用性,且BCS-Tree及其查询算法具有良好的检索效能.

基于异构环境的Out-Tree任务图的调度算法

分布式应用程序的有效调度是异构计算系统中的一个关键问题。目前已有的Out-Tree任务图的调度算法大多基于同构环境而开发,未考虑处理机的异构性,导致调度的效率较低。针对异构计算环境,提出一个基于列表和任务复制的Out-Tree任务图的静态启发式贪心调度算法,其时间复杂度为O(hv2 p),其中h、v和p分别表示任务图的高度、任务个数和调度使用的处理机个数。实验结果表明,相比其他算法,该算法能提供调度长度较短、处理机使用较少的有效调度,其应用性更强。

一种调度In-Tree任务图的算法

In-Tree任务图可用来表示归并、求和等分治算法的很多问题,该文针对这种任务图提出一种分层调度算法,利用队列存放被调度的任务,在同层任务调度中,优先把前驱不为空的任务调度到其一个前驱处理器上执行,只有前驱为空的任务才考虑是否分配新的处理器。实验表明,与以前的算法相比,该算法在调度长度相当的情况下,使用了更少的处理器。

Binary Tree Petersen网络性质及算法研究

基于Petersen图，提出了Binary Tree Petersen的网络结构，并对其特性进行了研究，证明了Binary Tree Petersen网络具有正则性以及良好的可扩展性，同时还具有比RP（k）、2-DToms更短的直径和良好的并行能力．另外，还基于Binary Tree Petersen网络分别给出了其上的单播和广播路由算法，证明了通信效率都为2j＋4．

实时分布系统中Out-Tree任务的调度与检查点策略

针对实时分布系统中的Out-Tree任务,提出了一种启发式的调度算法(HSA—OT),并开发了一种多处理机上的最优检查点策略。该调度算法能够保证任务的调度长度最小,所需处理器数目尽量少,没有处理机间通信开销。该检查点策略没有检查点全局一致性开销,可保证各处理机的失效率最低。

一个调度Out-Tree任务图的启发式算法

任务调度问题是并行分布式计算中的挑战性问题之一。大多数实际的调度算法是启发式的因而常常具有改进的余地。针对Out-Tree任务图这一基本结构提出一个基于任务复制的启发式调度算法,该算法在确保最短调度长度的同时,注重处理器的负载平衡,以达到节约处理器的目的。比较性实验的结果表明,该算法确保了最短调度长度且使用的处理器最少。因而,该算法提高了系统的利用率,避免消耗过多的资源,实际应用性更好。

一个调度Out-Tree任务图的新算法

OutTree任务图的调度研究可有效解决分治问题的并行计算。针对该类任务图,提出了一个新的调度算法。首先为各任务引入新定义,然后基于该定义计算各任务的优先级,进行调度。调度中,为节省处理器,在不改变调度长度的情况下,将任务尽可能地分配到已用处理器上。实验表明新算法的调度性能优于其他算法。

异构环境下Out-Tree任务图的调度算法

Out-Tree任务图是任务调度问题中的基本结构,现有的多数算法在调度该任务图时凸显出处理器浪费的问题,从而导致算法调度效果欠佳。针对该问题,结合任务复制的调度策略,提出一种基于平均值的启发式算法。该算法在不增加算法调度长度的情况下,尽可能将任务调度至已有的处理器中执行,注重平衡处理器的负载,达到减少使用处理器的目的。实验结果表明,与TDS算法相比,该算法使用的处理器个数较少,且效率较高。

基于复杂场景图的光线追踪渲染的Kd-tree构造

在基于光线跟踪等的全局光照绘制中,改良空间划分结构一直是各种加速策略中重要的方法之一。对常见的空间结构构建方法进行研究,针对复杂室内场景提出一种快速的分区构建方法。首先,算法并不直接将整个空间进行剖分,而是采用分组策略,结合包围盒进行判断,将具有一定空间联系的场景实体合并成一定数量的组;之后,对每个组使用优化后的Kd-tree构建细分结构,并提出合理的终止条件。与以往的方法相比,该方法构建的加速结构更适合于基于场景图构建的复杂室内环境,为快速生成真实感图形提供了有效的手段。

云环境下基于MKd-Tree的大规模图数据索引技术

由于高维属性和海量数据所带来的影响,数据管理需要相当高的计算负载,传统的集中索引技术已经变得不切实际。为满足数据的快速增长、海量和高维特性的要求,实现了一个高层次的分布式树形索引结构框架MRC-Tree。基于MRC-Tree框架基础上,提出了两种MKd-Tree索引结构构建方法,即OMKd-Tree和MMKd-Tree。理论分析和实验结果表明,基于MRC-Tree框架的MKd-Tree索引结构构建方法具有良好的可扩展性和较高的检索效率。