数据中心网络BCDC上的顶点独立生成树构造算法

作为云计算技术的基础,数据中心网络的通信性能成为了近年来的研究热点。独立生成树(Independent Spanning Trees, ISTs)作为数据中心网络中常见的基础结构,因其在可靠通信、容错广播以及安全分发方面的应用受到了研究者的广泛关注,在诸多特殊的网络上都取得了显著的成果。但是,学者们对在线图中独立生成树的研究却很少。BCDC是由Wang等于2018年提出的一个新的以服务器为中心的数据中心网络,其逻辑图是交叉立方体的线图且为2n-2正则图。文中给出了BCDC上独立生成树的构造算法,首先利用一种并行算法在交叉立方体中构造出2n-2棵树,然后将这些树按照一定规则连接并通过特定的转换方法将其转变为BCDC中2n-2棵相互独立的树,最后将BCDC中的剩余顶点通过一个时间复杂度为O(N)(其中N表示BCDC的顶点数)的高效算法挂接到树上,从而构造出BCDC上的以顶点[r,N(r,2)]为根的2n-2棵独立生成树,其中顶点r为交叉立方体CQ_n上的任意一个顶点。     

基于顶点度数的完全独立生成树研究

在计算机互连网络中,完全独立生成树在信息的可靠传输、并行传输、安全分发等方面具有重要的作用。假设图G中存在n棵生成树T₁,T₂,…,T_n,若对于图G中任意两个顶点u和v,满足u和v之间的路径在这n棵树中都是顶点不相交的,则称这n棵树为完全独立生成树(CISTs)。在2015年,Chang等人证明了对于包含n(n≥6)个顶点的任意图G,如果图G的最小顶点度数至少为n－2,那么,G中存在至少 n/3 棵CISTs[1]。在Chang等人的基础上,文中继续深入研究了图G中顶点度数和CISTs的棵数之间的关系。对于包含n(n≥5) 个顶点的任意图G,假设图G的最小顶点度数至少为n－2,得出度数为n－2的顶点的个数、度数为n－1的顶点的个数与图G中CISTs的棵数之间关系的推导等式,并证明了其正确性,从而改进了文献[1]中的结果。     

基于独立生成树的网络多路径传输方法研究

将高性能并行计算中的独立生成树理论应用到企业网络传输中,首先将企业网络拓扑抽象为互连网络,提出一种独立生成树可递归构造算法,生成多棵独立生成树,进而给出一种基于独立生成树的网络多路径传输方式,并在传输时间、传输速度上进行了网络传输性能分析,指出其优势。     

蜻蜓网络上完全独立生成树的构造算法

蜻蜓网络(Dragonfly network)是由Kim等提出的一种适用于高性能计算系统的拓扑结构。在蜻蜓网络中,网络被组织成两级架构,计算节点与交换机连接,交换机被分为成多个组。在每一组内部的每个交换机之间互相有一条边相连,任意两组之间有一条边相连接。完全独立生成树在信息的可靠传输、信息的并行传输和安全分发以及并行故障服务器诊断算法中具有非常重要的应用。在实际应用中,随着网络规模的不断增大,信息传输的效率以及安全性等要求越来越高。因此,研究网络的完全独立生成树具有重要意义。目前,有许多关于网络中完全独立生成树的研究,但是缺乏蜻蜓网络上的完全独立生成树的研究成果。文中提出了蜻蜓网络全局链路分别以相对链接、绝对链接以及循环链接下的完全独立生成树划分的构造算法,并在此划分的基础上给出了完全独立生成树边集合的构造算法,并对以上算法的正确性进行了证明。最后分析了算法的时间复杂度。     

弱连接边缘独立判别社交网络社区快速生成树推荐

针对传统社交网络社区推荐算法精度不高且计算复杂度过高的问题,提出一种弱连接边缘独立判别社交网络社区快速生成树检测算法,在提高社区推荐精度同时,降低算法计算复杂度。首先,结合社交网络社区推荐特点,设计基于边缘重量分配节点相似性的最大生成树算法,实现对社交网络社区的有效检测;其次,针对所提算法,存在弱连接边缘重复添加、删除,浪费计算资源的问题,提出弱连接边缘独立判别的快速生成树检测算法,进一步提高算法计算效率;最后,通过在标准测试数据库中的实验对比,验证了所提算法的有效性。     

大图数据上顶点驱动的并行最小生成树算法

最小生成树(minimum spanning tree, MST)是图论中最为经典算法之一.基于MST结构的聚类、分类和最短路径查询等复杂图算法,在效率和结果质量方面均有显著提高.然而,随着互联网的迅猛发展,图数据规模也变得越来越大,包含千万甚至上亿个顶点的大图数据越发常见.因此,如何在大图数据上实现查询处理和数据挖掘算法已成为亟待解决的问题之一.除此之外,由于大图数据的动态性特征,如何动态地维护算法结果也势必成为最受关注的问题之一.针对目前集中式的最小生成树算法无法解决海量和动态图数据的问题,首先提出了分区Prim(partition Prim, PP)算法,基于此提出了顶点驱动的并行MST算法——PB(PP Boruvka)算法,并论证了PB算法的正确性.另外,基于MapReduce和BSP框架实现了PB算法.针对只删除动态图特征,提出了MST维护算法,以实现高效的增量计算.对提出的计算和维护算法进行了代价分析和比较.最后,使用真实和模拟数据集,验证了PB算法和维护算法的有效性、高效性和可扩展性.     

一种新型无线传感器网络数据收集生成树

针对无线传感器网络精确数据收集,提出一种分布式生成树算法MLT.算法以一颗最小功率生成树为基础,在收集数据过程中不断统计节点剩余能量大小,找出瓶颈节点并与sink中存储的阈值比较,若低于阈值则转移瓶颈节点负担,优化树结构.研究表明随着阈值的增加网络生命周期先不断增大然后不断减小,阈值取值的合理性有效避免了因过于频繁变更树结构导致的额外能量消耗,使得所有节点能量较为均衡并延长了网络的生命周期,仿真实验验证了算法的有效性.     

一种基于生成树的无线传感器网络拓扑控制算法

文章主要介绍了一种基于生成树的无线传感器网络拓扑控制算法,通过限制代价较大的通信链路来解决网络的连通性与网络拓扑结构的稀疏性之间的矛盾。实验结果表明这是一种有效的拓扑结构控制方法,不仅能够保证了网络的稀疏性,而且能够有效的延长网络的生存周期。     

一种有效的最小生成树并行算法

本文基于三维网孔处理机阵列，运用分而治之策略和数据归约技术在加权无向图上给出了一种新的有效的最小生成树算法。     

一种无向图的生成树算法

求无向图的生成树是在网络和回路分析中经常遇到的重要问题。文章描述采用计算树的方法求解无向图的生成树,这种方法是通过列举生成树之间的差别来实现的。     

The number of spanning trees of the regular networks

The classic theorem on graphs and matrices is the Matrix-Tree Theorem, which gives the number of spanning trees t(G) of any graph G as the value of a certain determinant. However, in this paper, we will derive a simple formula for the number of spanning trees of the regular networks.     

An algorithm for geometric minimum spanning trees requiring nearly linear expected time

We describe an algorithm for finding a minimum spanning tree of the weighted complete graph induced by a set ofn points in Euclideand-space. The algorithm requires nearly linear expected time for points that are independently uniformly distributed in the unitd-cube. The first step of the algorithm is the spiral search procedure described by Bentleyet al. [BWY82] for finding a supergraph of the MST that hasO(n) edges. (The constant factor in the bound depends ond.) The next step is that of sorting the edges of the supergraph by weight using a radix distribution, or bucket, sort. These steps require linear expected time. Finally, Kruskal's algorithm is used with the sorted edges, requiringO(n(cn, n)) time in the worst case, withc>6. Since the function (cn, n) grows very slowly, this step requires linear time for all practical purposes. This result improves the previous bestO(n log log*n), and employs a much simpler algorithm. Also, this result demonstrates the robustness of bucket sorting, which requiresO(n) expected time in this case despite the probability dependency between the edge weights.     

字典乘积网络的支撑树计数

支撑树个数是边失效下网络可靠性分析与设计的一个重要性能参考指标,本文利用字典乘积的方法来构建网络,通过这种方法我们很容易由若干特定规模较小网络来构建规模较大的网络,并得到它的一个紧的支撑树计数解析公式,这样的计数公式仅仅依赖于小网络的性能参数,如:结点的度数、小网络的阶数、小网络的支撑树数目.     

There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees

Let S be a set ofn points in the plane. For an arbitrary positive rationalr, we construct a planar straight-line graph onS that approximates the complete Euclidean graph onS within the factor (1 + 1/r)[2/3 cos(/6)], and it has length bounded by 2r + 1 times the length of a minimum Euclidean spanning tree onS. Given the Deiaunay triangulation ofS, the graph can be constructed in linear time.     

On plane spanning trees and cycles of multicolored point sets with few intersections

Let P₁,…,Pk be a collection of disjoint point sets in R² in general position. We prove that for each 1?i?k we can find a plane spanning tree Ti of Pi such that the edges of T₁,…,Tk intersect at most , where n is the number of points in P₁∪?∪Pk. If the intersection of the convex hulls of P₁,…,Pk is nonempty, we can find k spanning cycles such that their edges intersect at most (k−1)n times, this bound is tight. We also prove that if P and Q are disjoint point sets in general position, then the minimum weight spanning trees of P and Q intersect at most 8n times, where |P∪Q|=n (the weight of an edge is its length).     

网络可存活生成树的快速恢复算法

如何应对网络链接失效是具有挑战性的问题之一,通常采用包含两棵生成树的可存活连接来预防链接失效。由于网络数据传输速率的高速增长,当两棵生成树的共享链接失效时,可存活连接中的生成树将全部失效。针对可存活连接中共享链接的失效提出了一种快速恢复算法,该算法通过搜索失效链接的可替换链接集,将失效概率最小的链接加入原可存活连接中的生成树,生成新的可存活连接。实验结果表明,该算法能够在显著降低恢复时间和时间复杂度的情形下,同时保证可存活连接的存活度接近当前网络的最优存活度。当网络节点数在10～100变化时,提出的算法比现有算法在恢复时间上的平均优化高达34.42%,同时在存活度上的误差不超过1%。     

Distributed hierarchical search for balanced energy consumption routing spanning trees in wireless sensor networks

We provide a new heuristic method approach to search for degree-balanced and small weight routing spanning trees in a network. The method is a modification of Kruskal’s minimum spanning tree search algorithm and is based on a distributed search by hierarchical clusters. It provides spanning trees with a lower maximum weighted degree, a bigger diameter, and can be used for balanced energy consumption routing in wireless sensor networks (WSN’s). The method can be naturally implemented in parallel or as a simple locally distributed algorithm. Simulations for a realistic case scenario WSN are done based on the transmission energy matrix. The simulation results show that the proposed approach can extend the functional lifetime of a WSN in terms of sensor transmission energy by 3–4 times. We also show that the results can be further improved by using a preliminary clustering of the input network.     

Maximizing the number of spanning trees of networks based on cycle basis representation

In this paper, we consider the problem of finding the graph topology of p vertices and q edges such that the resulting graph contains the maximum number of spanning trees. For any values of p and q, this problem still remains open. Only when q≧ p(p? l)/2 ? [p/2] it has been solved by Shier [4] and, recently, when q = p + 1 it has been solved by Wang and Wu [5]. In this paper, we shall formulate this problem into a nonlinear integer program by using the properties of the cycle bases of graphs. And then we shall show that this nonlinear integer program can be easily solved when q = p + 1 by applying our cycle basis approach. Consequently, we shall solve the nonlinear integer program when q = p + 2. Finally, concluding remarks will be given.     

The number of spanning trees of a graph with given matching number

The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. In this paper, we present sharp upper bounds for the number of spanning trees of a graph with given matching number.