A comparison of algorithms for origin–destination matrix generation on real road networks and an approximation approach

This paper considers the generation of the origin–destination (OD) matrix, basic data in any vehicle routing or traveling salesman problem. An OD matrix must be generated by calculating the shortest paths between some nodes. Candidate methods for this are repetitive use of one-to-all shortest path algorithms such as Dijkstra’s algorithm, use of all-to-all shortest path algorithms such as the Floyd–Warshall algorithm, and use of specifically designed some-to-some shortest path algorithms. This paper compares the performance of several shortest path algorithms in computing OD matrices on real road networks. Dijkstra’s algorithm with approximate bucket data structure performed the best for most of the networks tested. This paper also proposes a grouping-based algorithm for OD matrix generation. Although it is an approximation approach, it has several good characteristics: it can find the exact shortest distances for most OD pairs; it guarantees that all the calculated shortest path distance values have corresponding paths; the deviation of any distance from the corresponding true shortest distance is small; and its computation time is short.     

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.     

Termination Detection for Parallel Shortest Path Algorithms

Shortest path computation is required by a large number of applications such as VLSI, transportation, and communication networks. These applications, which are often very complex and have sparse networks, generally use parallel labeling shortest path algorithms. Such algorithms, when implemented on a distributed memory machine, require termination detection methods; these methods consist of some type of synchronization among all processors. Because global synchronization can be costly, it is assumed that the best termination detection methods synchronize as infrequently as possible. The frequency, however, can significantly impact the idle time of parallel labeling shortest path algorithms. In this paper we analyze the impact of this frequency on the performance, in particular the idle time, and identify when low versus high frequency detection is best. The analysis and results indicate that when the size of the subnetwork assigned to processor is small enough so that the computation time is less than or equal to the communication time within an iteration, high frequency termination detection methods should be used. Otherwise, low frequency methods should be used.     

A new parallel and distributed shortest path algorithm forhierarchically clustered data networks

This paper presents new efficient shortest path algorithms to solve single origin shortest path problems (SOSP problems) and multiple origins shortest path problems (MOSP problems) for hierarchically clustered data networks. To solve an SOSP problem for a network with n nodes, the distributed version of our algorithm reaches the time complexity of O(log(n)), which is less than the time complexity of O(log ² (n)) achieved by the best existing algorithm. To solve an MOSP problem, our algorithm minimizes the needed computation resources, including computation processors and communication links for the computation of each shortest path so that we can achieve massive parallelization. The time complexity of our algorithm for an MOSP problem is O(m log(n)), which is much less than the time complexity of O(M log² (0)) of the best previous algorithm. Here, M is the number of the shortest paths to be computed and m is a positive number related to the network topology and the distribution of the nodes incurring communications, m is usually much smaller than M. Our experiment shows that m is almost a constant when the network size increases. Accordingly, our algorithm is significantly faster than the best previous algorithms to solve MOSP problems for large data networks     

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。     

延迟的多径路由协议的改进

Ad hoc网络中多径路由算法因其表现出的较好性能受到人们越来越多的关注。但多径路由依旧采用“最小跳数”路由选择机制。很多研究显示最小跳数并不能提供最小的端到端时延保证。采用跨层设计思想,在路由选择机制中引入最短队列长度参数,提出了一种基于延迟的多路径路由算法QAOMDV。仿真结果表明QAOMDV算法可以降低端到端的传输时延,提高数据包的投递率,改善了网络性能。     

A survey of distributed optimization

In distributed optimization of multi-agent systems, agents cooperate to minimize a global function which is a sum of local objective functions. Motivated by applications including power systems, sensor networks, smart buildings, and smart manufacturing, various distributed optimization algorithms have been developed. In these algorithms, each agent performs local computation based on its own information and information received from its neighboring agents through the underlying communication network, so that the optimization problem can be solved in a distributed manner. This survey paper aims to offer a detailed overview of existing distributed optimization algorithms and their applications in power systems. More specifically, we first review discrete-time and continuous-time distributed optimization algorithms for undirected graphs. We then discuss how to extend these algorithms in various directions to handle more realistic scenarios. Finally, we focus on the application of distributed optimization in the optimal coordination of distributed energy resources.     

Stability routing with constrained path length for improved routability in dynamic MANETs

Quality of service (QoS) routing is known to be an NP-hard problem in case of two or more additive constraints, and several exact algorithms and heuristics have been proposed to address this issue. In this paper, we consider a particular two-constrained quality of service routing problem maximizing path stability with a limited path length in the quest of improving routability in dynamic multi-hop mobile wireless ad hoc networks. First, we propose a novel exact algorithm to solve the optimal weight-constrained path problem. We instantiate our algorithm to solve the most stable path not exceeding a certain number of hops, in polynomial time. This algorithm is then applied to the practical case of proactive routing in dynamic multi-hop wireless ad hoc networks. In these networks, an adequate compromise between route stability and its length in hops is essential for appropriately mitigating the impact of the network dynamics on the validity of established routes. Secondly, we set up a common framework for the comparison between three families of proactive routing: the shortest path-based routing, the most stable path-based routing and our proposed most stable constrained path routing. We show then through extensive simulations that routing based on our proposed algorithm selects appropriate stable paths yielding a very high routability with an average path length just above that of the shortest paths.     

低代价最短路径树快速算法的时间复杂度研究

低代价最短路径树是一种广泛使用的多播树,它能够在保证传送时延最小的同时尽量降低带宽消耗.快速低代价最短路径树算法FLSPT是在DDSP算法的基础上,通过改进节点的搜索过程,该算法构造的最短路径树与DDSP算法构造的树具有相同的性能,但其时间复杂度低于DDSP,其时间复杂度为O(nlog n e).FLSPT是利用Fibonacci堆来选择图中未计算点的最小值来计算时间复杂度的.通过对FLSPT的程序和Fibonacci堆的分析发现,用O(log(n!) e)来表示FLSPT算法的时间复杂度比文献[6]中分析的O(nlog(n) e)更能体现FLSPT算法高效率.