有向无环图的高效归约算法

将一个应用程序部署到给定的片上网络上执行时,需要将应用程序中的每一个子任务都指派给片上网络中的一个节点执行。该问题一般被建模成一组子任务作为顶点的有向无环图,任务在片上网络上的部署过程就等同于一个有向无环图的顶点向一个片上网络拓扑映射的过程。而随着应用程序和片上网络规模的增大,计算一个最优的映射方案是典型的难解问题。为了加速有向无环图到片上网络拓扑的映射过程,提出了有向无环图的归约算法,使归约后的图中的顶点数量尽可能地与给定片上网络中的节点数量相同。提出的图归约算法可以有效地识别出所有可归约子图,这些可归约子图可被归约为单一顶点。新算法的适用范围从嵌套图扩展到了任意图,并且拥有与原算法相同的复杂度量级。还提出了一种并行化的算法思想来加速可归约子图的搜索过程。     

基于有向无环图的互联网域内节能路由算法

互联网在快速发展的过程中面临新的挑战,其中网络能耗问题尤为突出。学术界提出了大量用于 解决网络能耗问题 的方案,然而这些方案都考虑了网络中的实时流量数据,计算复杂度较高,不利于实际部署。对此,提出一种基于有向无环图的互联网域内节能路由算法(Energy-efficient Intra-domain Routing Algorithm Based on Directed Acyclic Graph,EEBDAG),该方法 利用有向无环图来解决因链路关闭造成的路由环路和网络性能下降等问题, 仅须考虑网络拓扑结构,不需要考虑网络中的实时流量数据 。实验结果表明,EEBDAG不仅具有较低的节能比率,而且具有较低的链路利用率,为ISP解决互联网节能问题提供了一种全新的方案。     

经济模式下基于有向无环图的优化调度算法设计

Buyya提出的费用-时间优化算法运用经济规律把网格用户的任务映射到网格资源,但没有考虑任务间的优先关系。本文综合考虑时间、费用以及任务间的优先关系等诸多QoS需求,提出了基于有向无环图的优化调度算法。通过仿真实例,论证了该算法的优越性。     

基于有向无环图的成本-时间优化调度算法

网格计算环境下,基于有向无环图（DAG）的成本-时间优化调度算法运用经济规律把网格用户的任务映射到网格资源中运行。OGS算法考虑了任务间的优先关系,使得任务完成时间最小,但没考虑到在网格环境中所需的成本。Nimrod/G模型中提出基于时间和成本限制下的优化调度算法（DBC）考虑了时间和成本,但没考虑任务间的优先关系。本文综合考虑了成本-时间因素以及任务间的优先关系,在不增加完成时间的基础上,把任务映射到价格便宜的机器上,提出了基于有向无环图的成本-时间优化调度算法。通过仿真表明,相对OGS算法,该算法减少了所需成本。     

基于有向无环图网格独立任务调度算法*

提出了基于有向无环图多约束网格环境下独立任务的调度模型,为其建立多约束线性规划模型,通过求解模型节点的优先级,获得网格各计算节点最优任务调度数;然后基于多约束最优任务调度方案,提出多约束带宽优先启发式算法(MCOPBHATS)和多约束计算速度优先启发式算法(MCOPCHATS)。实验结果表明,在多约束异构的网格环境下实现大量独立任务调度时, MCOPBHATS和MCOPCHATS算法的性能优于基于多约束最优任务调度方案的MinMin 算法。     

基于有向无环图的成本-时间优化调度算法

网格计算环境下,基于有向无环图(DAG)的成本-时间优化调度算法运用经济规律把网格用户的任务映射到网格资源中运行.OGS算法考虑了任务间的优先关系,使得任务完成时间最小,但没考虑到在网格环境中所需的成本.Nimrod/G模型中提出基于时间和成本限制下的优化调度算法(DBC)考虑了时间和成本,但没考虑任务问的优先关系.本文综合考虑了成本-时间因素以及任务间的优先关系,在不增加完成时间的基础上,把任务映射到价格便宜的机器上,提出了基于有向无环图的成本-时间优化调度算法.通过仿真表明,相对OGS算法,该算法减少了所需成本.     

面向对象的流程工业系统有向无环图建模

提出流程工业系统中有向无环图的面向对象的建模方法。介绍使用面向对象的技术对流程工业系统模进行建模的关键要素的技巧,定义描述流程工业系统中有向无环图模型的建模机制,扩展流程工业系统模型所具有的特性。以流程工业系统出现异常时的诊断实例说明系统模型解决问题的有效性。     

异质信息网络中基于有向无环图的影响力最大化算法

针对异质信息网络中的影响力最大化(IM)问题,提出了一种基于有向无环图(DAG)的影响力最大化算法(DAGIM).首先基于DAG结构度量节点的影响力,然后采用边际增益策略选择影响力最大的节点.DAG结构表达力强,不仅描述了不同类型节点之间的显性关系,也刻画了节点之间的隐性关系,较完整地保留了网络的异质信息.在三个真实数...     

一个新的无向图画图算法

将一般无向图的画图问题转化为函数优化问题,用遗传算法求目标函数的最优解的近似值,从而得到无向图自动画图算法的一个一般框架.新方法的特点是:不同的画图算法的框架都一样,所不同的只是反映无向图画图问题的美观标准的目标函数.其优点在于,算法统一、方法简单、容易实现、便于修改,并且易于并行化,可以直接用来画非连通图.     

一种基于有向无环图的本体内聚度度量方法

目前,随着本体的广泛使用和快速发展,本体在结构与语义上变得越来越复杂。如何对本体的质量进行评估成为本体构建和重用的主要问题。在本体构建过程中,对本体进行评估有利于对本体进行重构和优化,以构建高质量的本体。在本体重用过程中,可以帮助用户在候选本体集中选择最优结构的本体。提出一种基于有向无环图(DAG)的本体内聚度度量方法,首先依据有向无环图的结构提出一组本体内聚度度量指标;然后根据已有的度量验证框架对其进行验证,说明度量指标在理论上有效;最后使用经典本体数据集进行实验,说明所提出的本体内聚度度量方法的合理性和有效性,有利于本体的构建和重用。     

利用遗传算法改进DAG绘制的方法

DAG图（Directed Acyclic Graph）广泛应用于数据库建模、工程设计等领域。DAG图一般用矩阵来存储,能够将矩阵存储的DAG图正确、美观地画出来,使得DAG图更直观,清晰,方便各种问题的分析和处理。DAG图的绘制包含分层、最小化边交叉数和删除哑结点。提出了基于遗传算法的分层和最小化边交叉数的方法和删除哑结点的启发式算法。实例结果表明提出的方法能有效解决DAG图绘制中的交叉点问题。     

有向无环图上k步可达查询优化算法

k步可达查询用于在给定的有向无环图（DAG）中回答两点之间是否存在长度不超过k的路径。针对现有方法的索引规模大、查询处理效率低的问题,提出一种基于部分点的双向最短路径索引来提升索引的可达信息覆盖率,并提出一组优化规则来减小索引规模;然后提出基于简化图的正反互逆拓扑索引来加速回答不可达查询;最后提出远距离优先的双向遍历策略来提高查询处理的效率。基于21个真实数据集（如引用网络、社交网络等）的实验结果表明,相比已有的高效方法PLL及BFSI-B,所提出的算法具有更小的索引规模和更快的查询响应速度。     

Performance analysis of parallel programs based on directed acyclic graphs

Task precedence graphs are widely used for modeling and evaluation of parallel applications. Their nodes represent the subtasks of the parallel program and the edges represent the precedence relations between the subtasks. The execution times of the subtasks are described by random variables and their distributions. In our paper we introduce a new class of distributions, particularly suited for the modeling and evaluation of parallel programs. Exponential polynomials introduced by Sahner and Trivedi have the disadvantage that a large number of parameters is needed for the representation of realistic task execution times, which usually have a small value of variation. We extend this class to derive the class of truncated -exponential polynomials which allow the representation of realistic task execution times with fewer parameters. Additionally this class of distributions has the advantage that minimum as well as maximum execution times can be guaranteed. Models with a large number of subtasks can not be evaluated on a computer using exact analytical methods because of memory requirements and numerical inaccuracies, which accumulate, when the operations of analysis are applied. Using extreme value theory we derive approximate formulas for the parallel independent execution of subtasks, a structure, which can be found in every parallel program. The obtained results for truncated and not truncated distributions show, that distributions with an infinite domain are not suitable, particularly for massively parallel structures. Received: 26 August 1994 / 13 May 1996     

A technique for drawing directed graphs

A four-pass algorithm for drawing directed graphs is presented. The fist pass finds an optimal rank assignment using a network simplex algorithm. The seconds pass sets the vertex order within ranks by an iterative heuristic, incorporating a novel weight function and local transpositions to reduce crossings. The third pass finds optimal coordinates for nodes by constructing and ranking an auxiliary graph. The fourth pass makes splines to draw edges. The algorithm creates good drawings and is fast     

Convergent drawing for mutually connected directed graphs

Directed graphs are used to represent a variety of datasets, including friendship on social networking services (SNS), pathways of genes, and citations of research papers. Graph drawing is useful in representing such datasets. At the international conference on Information Visualization (IV), we have presented a convergent edge drawing and a node layout technique for tightly and mutually connected directed graphs. The edge drawing technique in the IV paper includes three features: ordinary bundling of edges connecting pairs of node clusters, convergence of multiple bundles that connect to the same node cluster, and shape adjustment of two bundles connecting the same pair of node clusters. In this paper, we present improved node layout and edge drawing techniques, which make our edge bundling more effective. This paper also introduces a case study with a directed paper citation graph dataset.vvvvv     

Efficient coding of labeled directed acyclic graphs

 We use an adaptation of the Prüfer code for trees to encode labeled directed acyclic graphs, which are often abbreviated to DAGs (or ADGs). In this paper, each DAG is assigned a unique DAG code, which allows an easy handling for several purposes. The set of all possible DAG codes (and therefore the set of all DAGs) for a fixed number of n vertices can be generated efficiently. Furthermore, we are able to rank DAGs, i.e., we provide an algorithm that assigns every DAG a unique number in the set {0,…,a _n −1}, where a _n is the cardinality of the set of labeled DAGs with n≥1 vertices, and we are able to unrank DAGs, which is the inverse operation. We also gain recurrence relations, which can be used to calculate a _n and a _n,q , i.e., the number of DAGs with n vertices and q edges. Finally, it is possible to generate, enumerate, rank and unrank DAGs with given number of edges and also DAGs with bounded indegree. RID="*" ID="*" This research was supported by the Austrian Science Fund (FWF), P13261-INF. I want to thank the reviewers, specially the one who suggested to add the algorithm for unranking DAG codes, for reading the paper very carefully and for the helpful comments.     

Topological additive numbering of directed acyclic graphs

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let D be a digraph and f   a labeling of its vertices with positive integers; denote by S(v)$S(v)$ the sum of labels over all neighbors of each vertex v. The labeling f is called topological additive numbering   if S(u)<S(v)$S(u)<S(v)$ for each arc (u,v)$(u,v)$ of the digraph. The problem asks to find the minimum number k for which D   has a topological additive numbering with labels belonging to {1,…,k}$\{1,\dots ,k\}$, denoted by _ηt(D)${\eta }_t(D)$.     

Solving shortest paths efficiently on nearly acyclic directed graphs

Shortest path problems can be solved very efficiently when a directed graph is nearly acyclic. Earlier results defined a graph decomposition, now called the 1-dominator set, which consists of a unique collection of acyclic structures with each single acyclic structure dominated by a single associated trigger vertex. In this framework, a specialised shortest path algorithm only spends delete-min operations on trigger vertices, thereby making the computation of shortest paths through non-trigger vertices easier. A previously presented algorithm computed the 1-dominator set in O(mn) worst-case time, which allowed it to be integrated as part of an O(mn+nrlogr) time all-pairs algorithm. Here m and n respectively denote the number of edges and vertices in the graph, while r denotes the number of trigger vertices. A new algorithm presented in this paper computes the 1-dominator set in just O(m) time. This can be integrated as part of the O(m+rlogr) time spent solving single-source, improving on the value of r obtained by the earlier tree-decomposition single-source algorithm. In addition, a new bidirectional form of 1-dominator set is presented, which further improves the value of r by defining acyclic structures in both directions over edges in the graph. The bidirectional 1-dominator set can similarly be computed in O(m) time and included as part of the O(m+rlogr) time spent computing single-source. This paper also presents a new all-pairs algorithm under the more general framework where r is defined as the size of any predetermined feedback vertex set of the graph, improving the previous all-pairs time complexity from O(mn+nr²) to O(mn+r³).