网络最短路问题的改进算法

本文着重研究著名的Dijkstra网络最短路算法的实现效率，提出算法实现的若干技巧，大大提高了Dijkstra最短路算法的适用性和时间空间效率。     

无回路网络中最短路问题的高效算法

无回路网络是一类重要的网络,给出在无回路网络中求解最短路树形图和任意顶点对间最短路的高效算法。该算法将顶点进行重新编号,结合广度优先探索法,从源顶点出发依次搜索每个顶点的所有出弧,并在弧的头部进行权值变换操作,可以得到最短路树形图和任意顶点对间最短路,算法复杂度分别为O(m)和O(m(n-m1/2))。该算法思想简便、复杂度低、易于操作。 关键词：     

最短路问题的Floyd加速算法与优化

Floyd算法是求解网络中任意两点之间最短路的高效算法,文章给出了在不含负回路的网络中Floyd加速算法及优化方法,并构造了求解最短路径的序号矩阵。算法分析和计算实例表明,优化后的Floyd加速算法迭代速度快,计算量大大减少,路径寻找简单、直观。     

最短路问题的Floyd改进算法

目前在不含负回路的网络中,对于求解任意两节点之间最短路问题的方法有很多,Floyd算法是最经典的算法之一,但随着节点数量的增加,重复的计算量也随之增大,从而降低了计算效率。为此,文中通过迭代矩阵和下标标注法对Floyd算法进行了改进,改进后的算法既能快速地计算出网络中任意两节点之间的最短路长值,又能更直观地找出最短路径。通过具体实例分析表明,Floyd改进算法减少了重复计算,简化了路径标注方法,提高了计算效率。     

改进的进化算法解最短路问题

最短路问题是组合优化中的经典问题之一,对其设计有效的算法具有广泛的应用价值和重要的理论意义．为了减少对初始种群选取的限制,扩大种群的多样性,本文提出了一种新的杂交方式．根据一对染色体中不同位相同基因对的数目,设计了分类杂交．这种杂交不仅增加了种群的多样性,还避免了不可行解的出现．与杂交算子相对应设计了具有局部搜索功能的收缩—扩张式变异算子,使得本算法效率有了极大提高,并在理论上证明该算法以概率1收敛到全局最优解．最后的数值试验也表明此算法是十分有效的．     

最短路问题的改进算法

通过引入两个数组,从提高算法效率和增强寻路直观性两个方面对无回路网络最短路问题的权矩阵法进行了改进.改进后的算法既能快速的计算从源节点到其目的节点的最短路权又能更直观的找出最短路.最后算法分析和仿真结果表明,改进算法较权矩阵法相比,运算速度有了明显的提高,是计算无回路网络最短路的一种有效算法.     

基于节点合并的最短路问题新算法

提出一个解决非负权网络最短路问题的节点合并算法.该算法以将距离起始节点最近的邻居节点拉到身边的方法,与距离最近节点不断合并,重复这一动作,最终求得起始节点到其他节点的最短路距离.与Dijkstra算法相比,节点合并算法不存在节点着色操作,始终只考虑起始节点的邻居,实现步骤更加简单,整个过程可以采用向量化操作,易于理解和编程实现.数据试验表明,节点合并算法求解效率明显高于Dijkstra算法.     

基于MPI的中国教育网最短路并行算法

针对传统的Floyd算法难以解决中国教育网的平均最短路径长度计算问题,在对网络进行度分析的基础上,设计了一种宽度优先搜索(BFS)并行算法,该算法可有效地避免对出度为0的节点进行搜索,采用VC编写基于MPI(MessagePassingInterface)的并行程序,通过20台电脑连网计算分析,该方法取得了令人满意的结果。     

构造已知核度的最短网络的近似算法

在网络的优化设计中,可靠性和经济性是测度网络优劣的两个重要标准.而可靠性与经济性是此消彼长的关系,即可靠性越高,成本越大,经济性越差.该文在系统核与核度理论的基础上,给出度量网络可靠性的一种新方法.并在网络的可靠性一定--即核度已知的条件下,给出构造最短网络的近似算法,算法的时间复杂性是O(n).这对网络优化设计和网络的组织规划具有重要的理论指导意义.     

紧急事件的动态交通流模型及双向动态最短路诱导算法

针对城市快速路的交通紧急事件给出了宏观的动态交通流模型,在METANET模型的基础上考虑紧急事件所占用车道数、进出口匝道及诱导信息对模型的影响,同时针对交通紧急事件的及时有效处理,给出了一种双向动态的最短路径诱导算法,在此算法中,节点间的权值是随着高速路的路面状况及交通拥堵情况等变化的动态函数,故在紧急事件处理中从两个方向搜索最短路,其过程是动态的,实时的,为紧急事件的及时处理和有效的救援争取了时间。通过仿真对比,证明了此算法的可行性,有效性,同时证明了此算法的搜索效率也得到了较大提高。     

时间依赖的网络中最小时间路径算法

时间依赖的网络与传统网络模型相比更具有现实意义,具有广泛的应用领域,交通网络和通信网络可以抽象为时间依赖的网络模型,当模型中弧的工度是时间依赖的变量,最短路径问题的求解变得非常困难,早期的研究者通过具体的网络实例认识到传统最短路径算法在这种情况下是不正确的,因此给出限制性条件使得传统最短路径算法是有效的。该文从最短路径算法的理论基础入手,从理论上证明了传统最短路径算法,如Dijkstra算法和标号设置算法,在时间依赖的网络上不能有效地求解最短路径问题,并且,在没有任何限制性条件下,给出了时间依赖的网络模型,理论基础,求解最小时间路径的优化条件和SPTDN算法,从理论上证明了SPTDN算法的正确性,算法的实验结果是正确的,最后给出了时间依赖的网络应用实例。     

Algorithmic Techniques for Maintaining Shortest Routes in Dynamic Networks

In this paper, we survey algorithms for shortest paths in dynamic networks. Although research on this problem spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. In this survey, we will make a special effort to abstract some combinatorial and algebraic properties, and some common data-structural tools that are at the base of those techniques. This will help us try to present some of the newest results in a unifying framework so that they can be better understood and deployed also by non-specialists.     

带权区间图的最短路算法

提出一个解带权区间图的最短路问题的O(nα(n))时间新算法，其中n是带权区间图中带权区间的个数，α(n)是单变量Ackerman函数的逆函数，它是一个增长速度比log n慢得多的函数，对于通常所见到的n，α(n)≤4．本文提出的新算法不仅在时间复杂性上比直接用Dijkstra算法解带权区间图的最短路问题有较大改进，而且算法设计思想简单，易于理解和实现．     

Parallel Algorithms for Dynamic Shortest Path Problems

The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster‐than‐real‐time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst‐case running‐time complexity. This implies that no algorithm with a better worst‐case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all‐to‐one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially‐available high‐performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared‐memory and two message‐passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message‐passing environment based on the parallel virtual machine (PVM) library and a multi‐threading environment based on the SUN Microsystems Multi‐Threads (MT) library. We also develop a time‐based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ‘ideal’ theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distributed network of Unix workstations and a SUN shared‐memory machine containing eight processors. Satisfactory speed‐ups in the running time of sequential algorithms are achieved, in particular for shared‐memory machines. Numerical results indicate that shared‐memory computers constitute the most appropriate type of parallel computing platforms for the computation of dynamic shortest paths for real‐time ITS applications.     

GIS时变权值网络最短路径算法研究

最短路径分析是GIS网络分析的基础。传统的最短路径算法中,比较经典的算法是Dijkstra算法。由于地理信息系统中的数据具有不确定性、数据量庞大等特点,因此采用传统的Dijkstra算法进行最短路径分析就不适应。为此本文分析了传统网络中的最短路径算法-Dijkstra算法在时变权值网络结构中的局限性,给出了一种适应于时变权值网络的最短路径算法,并且利用改进的邻接表作为存储结构对算法进行了优化。     

基于混沌神经网络的最短路径路由算法

飞速发展的计算机网络对路由算法的反应速度提出了更高的要求．神经网络作为一种新的组合优化计算工具。在网络路由方面的应用得到较大关注．与传统的采用串行执行方式的算法相比,神经网络路由算法以其固有的并行执行方式,以及潜在的硬件实施能力,将成为这一领域的有力竞争者．由此提出了一种基于混沌神经网络的最短路径路由算法．仿真结果表明,该算法能有效克服Hopfield神经网络易陷入局部最优解的缺点,并且在收敛速度方面有了很大改进．     

Engineering a New Algorithm for Distributed Shortest Paths on Dynamic Networks

We study the problem of dynamically updating all-pairs shortest paths in a distributed network while edge update operations occur to the network. We consider the practical case of a dynamic network in which an edge update can occur while one or more other edge updates are under processing. A node of the network might be affected by a subset of these changes, thus being involved in the concurrent executions related to such changes. In this paper, we provide a new algorithm for this problem, and experimentally compare its performance with respect to those of the most popular solutions in the literature: the classical distributed Bellman-Ford method, which is still used in real network and implemented in the RIP protocol, and DUAL, the Diffuse Update ALgorithm, which is part of CISCO’s widely used EIGRP protocol. As input to the algorithms, we used both real-world and artificial instances of the problem. The experiments performed show that the space occupancy per node required by the new algorithm is smaller than that required by both Bellman-Ford and DUAL. In terms of messages, the new algorithm outperforms both Bellman-Ford and DUAL on the real-world topologies, while on artificial instances, the new algorithm sends a number of messages that is more than that of DUAL and much smaller than that of Bellman-Ford.     

Exact and Approximate Truthful Mechanisms for the Shortest Paths Tree Problem

Let a communication network be modeled by an undirected graph G=(V,E) of n nodes and m edges, and assume that edges are controlled by selfish agents. In this paper we analyze the problem of designing a truthful mechanism for computing one of the most popular structures in communication networks, i.e., the single-source shortest paths tree. More precisely, we will study several realistic scenarios, in which each agent can own either a single or multiple edges of G. In particular, for the single-edge case, we will show that: (i) in the classic utilitarian case, the problem can be solved efficiently in O(mnlog α(m,n)) time, where α(m,n) is the inverse of the Ackermann’s function; (ii) in a meaningful non-utilitarian case, namely that in which agents’ valuation functions only depend on the edge lengths, the problem can be solved in O(m+nlog n) time. Conversely, for the multiple-edges case, we will show in the utilitarian case an O(mP+nPlog n) time truthful mechanism, where P=O(n) denotes the number of agents participating in the solution, while in the same non-utilitarian case we will prove a general lower bound to the approximation ratio that can be achieved by any truthful mechanism, by showing that no c-approximate mechanism can exist, for any fixed . Work partially supported by the Research Project GRID.IT, funded by the Italian Ministry of Education, University and Research. Part of the results herein contained was presented at the 11th International Euro-Par Conference (Euro-Par’05), Lisbon, Portugal, 2005.