Modelica建模软件中拓扑排序相关算法研究

为了提高现有OpenModelica软件对DAE系统的预处理模块中求强连通分量与拓扑排序部分的性能,提出了基于Kosaraju算法实现的策略.阐述了Modelica软件的实现原理,叙述了拓扑排序相关算法在其中的重要性,分析了现有Modelica 软件中使用的求强连通分量与拓扑排序部分的算法,比较了Tarjan算法的实现方案与Kosaraju算法实现方案.对两种方案进行了比较和分析结果,表明了Kosaraju算法方案的可行性和有效性.     

一个带环检测的深度优先搜索拓扑排序算法

提出了一种带环检测功能的深度优先搜索拓扑排序算法,详细介绍了几种基本拓扑排序算法,分析了带环检测功能的深度优先搜索拓扑排序算法的意义和作用,并证明了该算法的完备性和正确性,给出了该算法的用C++编写的实现代码。     

关于强连通子图的排序算法

本文给出了一个强连通子图的排序算法,证明了算法的正确性。其算法的时间复杂度为O(m~2)。该算法将一般排序方法引入到图论中,使难于实现的图排序简化为整数排序。     

AOV网中全拓扑排序算法的设计及应用

以顶点表示活动的网络(AOV网)可用来表示整个工程中各个子工程的先后次序制约关系,利用拓扑排序算法能求得子工程的线性序列———拓扑序列。按此序列安排各子工程,能保证整个工程的顺利完成。传统的拓扑排序算法基于栈结构实现,只能求得实际存在的多个拓扑序列中的一种,削弱了算法的实用价值。文中为了弥补这一缺陷,设计全拓扑排序算法求出了AOV网中实际存在的全部拓扑序列。给出了AOV网的定义及拓扑排序算法思想,分析了传统拓扑算法的不足,提出了一个全拓扑排序求解算法。并讨论了算法中用到的数据结构,以及算法的伪代码实现,通过一个应用实例验证了全拓扑排序算法的实用性和正确性。     

AOV网中全拓扑排序算法的设计及应用

以顶点表示活动的网络(AOV网)可用来表示整个工程中各个子工程的先后次序制约关系,利用拓扑排序算法能求得子工程的线性序列--拓扑序列.按此序列安排各子工程,能保证整个工程的顺利完成.传统的拓扑排序算法基于栈结构实现,只能求得实际存在的多个拓扑序列中的一种,削弱了算法的实用价值.文中为了弥补这一缺陷,设计全拓扑排序算法求出了AOV网中实际存在的全部拓扑序列.给出了AOV网的定义及拓扑排序算法思想,分析了传统拓扑算法的不足,提出了一个全拓扑排序求解算法.并讨论了算法中用到的数据结构,以及算法的伪代码实现,通过一个应用实例验证了全拓扑排序算法的实用性和正确性.     

一种新的基于邻接矩阵的拓扑排序算法

为了降低基于邻接矩阵的拓扑排序算法的复杂性，将单顶点算法框架扩展成集合算法框架，给出一些便于进行拓扑排序的有向无环图的性质。在此基础上，定义了适合进行弧删除操作和无前驱顶点判断的邻接矩阵运算，给出了有向弧邻接矩阵的存储方案，最终提出了一种时间和空间复杂度都比较低的拓扑排序算法。     

贪婪算法之拓扑排序的实现

拓扑排序是图的应用领域中一种重要运算,可以根据拓扑序列串行地安排活动。本文给出了拓扑排序的贪婪算法．讨论了算法中用到的数据结构．本文采用邻接袁和栈以C＋＋语言进行仿真．给出了仿真结果。     

拓扑排序在并发控制可串行化算法中的应用

并发控制是分布式数据库管理系统的重要组成部分,并发控制用来控制多个事务的并发运行,避免它们之间的相互干扰,保证每个事务都产生正确的结果。该文从构造并发控制可串行化的前趋图出发,利用拓扑排序进一步研究了并发控制可串行化的算法,详细阐述了冲突可串行和状态可串行化的测试算法并运用在实例中。该算法可以作为并发控制可串行化的正确性准则,在实际中,应结合其它算法共同运用。     

并行拓扑排序算法PTSA的设计与实现

文章对AOV网首次提出了一种基于层次的混合数据结构,按分层处理的方法实现并行拓扑排序算法PTSA,求得了AOV网中顶点的所有拓扑序列,克服了以往基于栈结构只能求得一种拓扑序列的缺陷。PTSA算法为工程中各子工程的串行或并行安排提供了确定的选择,提升了拓扑排序算法的实用价值。     

求强连通分量的几种算法的实现与分析

有向图的强连通性是图论中的经典问题,有着很多重要的应用。该文给出了求强连通分量的Kosaraju、Tarjan和Gabow三个算法的具体实现,并对算法的效率进行了分析。     

On the Complexity of Strongly Connected Components in Directed Hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (Sccs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any components but themselves). Almost linear here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor α(n), where α is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all Sccs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the Sccs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the Sccs is harder in directed hypergraphs than in directed graphs.     

On Enumerating Minimal Dicuts and Strongly Connected Subgraphs

We consider the problems of enumerating all minimal strongly connected subgraphs and all minimal dicuts of a given strongly connected directed graph G=(V,E). We show that the first of these problems can be solved in incremental polynomial time, while the second problem is NP-hard: given a collection of minimal dicuts for G, it is NP-hard to tell whether it can be extended. The latter result implies, in particular, that for a given set of points , it is NP-hard to generate all maximal subsets of contained in a closed half-space through the origin. We also discuss the enumeration of all minimal subsets of whose convex hull contains the origin as an interior point, and show that this problem includes as a special case the well-known hypergraph transversal problem. This research was supported by the National Science Foundation (Grant IIS-0118635). The third and fourth authors are also grateful for the partial support by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science. Our friend and co-author, Leonid Khachiyan tragically passed away on April 29, 2005.     

An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps

We present a symbolic algorithm for strongly connected component decomposition. The algorithm performs Θ(n log n) image and preimage computations in the worst case, where n is the number of nodes in the graph. This is an improvement over the previously known quadratic bound. The algorithm can be used to decide emptiness of Büchi automata with the same complexity bound, improving Emerson and Lei's quadratic bound, and emptiness of Streett automata, with a similar bound in terms of nodes. It also leads to an improved procedure for the generation of nonemptiness witnesses. This work was supported in part by SRC contract 98-DJ-620 and NSF grant CCR-99-71195. This work was done while the author was at the University of Colorado at Boulder.     

基于连通分支的聚类分析算法及其在铝电解中的应用

提出了一种基于连通分支的聚类分析算法,用以解决铝电解工业生产中槽况的分类问题。该聚类分析算法的核心是根据点的距离构建空间的连通分支,并利用时间窗口的滑动来判断当前的槽况。文中详细讨论了算法的基本概念,并给出了相应的CC_CTL挖掘算法。     

基于DAG的拓扑排序改进算法及在BOM中的运用

文章讨论了传统的BOM防止嵌套错误算法和低层码计算的算法的实现过程。在分析算法的实现过程后对其原理进行评价的基础上,将BOM树结构和DAG图性质进行比较后对这两种算法进行改进,提出了一种蕴涵了拓扑排序思想的算法。最后编程实现了此算法的伪代码,该算法在实际运用中取得了明显的效果,减少了数据库系统资源的占用,大大提高了数据库的性能和响应能力。