A parallel shortest path algorithm

A new algorithm to find the shortest path between a pair of nodes is presented. In one hand this algorithm expands the search from origin and destination simultaneously, on the other hand it uses a lower bound for the shortest path to guide this search. Computational comparisons with existing algorithms show its efficiency. The implementation on a parallel computer is also discussed.     

A neural network for shortest path computation

This paper presents a new neural network to solve the shortest path problem for inter-network routing. The proposed solution extends the traditional single-layer recurrent Hopfield architecture introducing a two-layer architecture that automatically guarantees an entire set of constraints held by any valid solution to the shortest path problem. This new method addresses some of the limitations of previous solutions, in particular the lack of reliability in what concerns successful and valid convergence. Experimental results show that an improvement in successful convergence can be achieved in certain classes of graphs. Additionally, computation performance is also improved at the expense of slightly worse results.     

A hill-jump algorithm of Hopfield neural network for shortest path problem in communication network

In this paper, we present a hill-jump algorithm of the Hopfield neural network for the shortest path problem in communication networks, where the goal is to find the shortest path from a starting node to an ending node. The method is intended to provide a near-optimum parallel algorithm for solving the shortest path problem. To do this, first the method uses the Hopfield neural network to get a path. Because the neural network always falls into a local minimum, the found path is usually not a shortest path. To search the shortest path, the method then helps the neural network jump from local minima of energy function by using another neural network built from a part of energy function of the problem. The method is tested through simulating some randomly generated communication networks, with the simulation results showing that the solution found by the proposed method is superior to that of the best existing neural network based algorithm.     

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     

A shortest path routing algorithm for incomplete WK-recursivenetworks

The WK-recursive networks own two structural advantages: expansibility and equal degree. A network is expansible if no changes to node configuration and link connection are necessary when it is expanded, and of equal degree if its nodes have the same degree no matter what the size is. However, the number of nodes contained in a WK-recursive network is restricted to d^t, where d>1 is the size of the basic building block and t⩾1 is the level of expansion. The incomplete WK-recursive networks, which were proposed to relieve this restriction, are allowed to contain an arbitrary number of basic building blocks, while presenting the advantages of the WK-recursive networks. Designing shortest-path routing algorithms for incomplete networks is in general more difficult than for complete networks. The reason is that most incomplete networks lack a unified representation. One of the contributions of this paper is to demonstrate a useful representation, i.e., the multistage graph representation, for the incomplete WK-recursive networks. On the basis of it, a shortest-path routing algorithm is then proposed. With O(d·t) time preprocessing, this algorithm takes O(t) time for each intermediate node to determine the next node along the shortest path     

求解最短路径的遗传算法中若干问题的讨论

针对道路交通网络中的最短路径问题,讨论了遗传算法中遗传算子的设计及运行参数的选择,提出一种新的交叉算子,提高了种群多样性.通过计算机仿真实验,比较了多种遗传算子设计方案的优劣及不同运行参数对算法效果的影响,为实际应用提供了参考.采用VC语言实现该遗传算法,并应用于实际的电子地图中,结果表明了算法的有效性和实用性.     

闭合螺线阵列的最短路径算法

介绍了闭合螺线阵列的概念;利用动态规划法中的Floyd算法思想对求解闭合螺线阵列最短路径的问题进行了描述,并给出了具体算法;给出了利用二维数组算法求解闭合螺线阵列最短路径的过程.对于以上两种算法的优缺点进行了比较.这两种算法可以用于解决大多数路径问题.     

一种求受顶点数限制的最短路径的新算法

提出了一种基于逆邻接表求受顶点数限制的最短路径的新算法,其时间复杂度为O(m-2)^*w)(m是受限制的顶点数,w是有向图中弧的条数),优于同类算法。采用逆邻接表作为图的存储结构,该算法很容易实现。     

Hybrid shortest path algorithm for vehicle navigation

Vehicle navigation is one of the important applications of the single-source single-target shortest path algorithm. This application frequently involves large scale networks with limited computing power and memory space. In this study, several heuristic concepts, including hierarchical, bidirectional, and A^*, are combined and used to develop hybrid algorithms that reduce searching space, improve searching speed, and provide the shortest path that closely resembles the behavior of most road users. The proposed algorithms are demonstrated on a real network consisting 374,520 nodes and 502,485 links. The network is preprocessed and separated into two connected subnetworks. The upper layer of network is constructed with high mobility links, while the lower layer comprises high accessibility links. The proposed hybrid algorithms are implemented on both PC and hand-held platforms. Experiments show a significant acceleration compared to the Dijkstra and A^* algorithm. Memory consumption of the hybrid algorithm is also considerably less than traditional algorithms. Results of this study showed the hybrid algorithms have an advantage over the traditional algorithm for vehicle navigation systems.     

A novel neural network method for shortest path tree computation

Shortest path tree (SPT) computation is a critical issue in many real world problems, such as routing in networks. It is also a constrained optimization problem, which has been studied by many authors in recent years. Typically, it is solved by heuristic algorithms, such as the famous Dijkstra's algorithm, which can quickly provide a good solution in most instances. However, with the scale of problem increasing, these methods are inefficient and may consume a considerable amount of CPU time. Neural networks, which are massively parallel models, can solve this question easily. This paper presents an efficient modified continued pulse coupled neural network (MCPCNN) model for SPT computation in a large scale instance. The proposed model is topologically organized with only local lateral connections among neurons. The start neuron fires first, and then the firing event spreads out through the lateral connections among the neurons, like the propagation of a wave. Each neuron records its parent, that is, the neighbor which caused it to fire. It proves that the generated wave in the network spreads outward with travel times proportional to the connection weight between neurons. Thus, the generated path is always the global optimal shortest path from the source to all destinations. The proposed model is also applied to generate SPTs for a real given graph step by step. The effectiveness and efficiency of the proposed approach is demonstrated through simulation and comparison studies.     

A constrained binary knapsack approximation for shortest path network interdiction

A modified shortest path network interdiction model is approximated in this work by a constrained binary knapsack which uses aggregated arc maximum flow as the objective function coefficient. In the modified shortest path network interdiction problem, an attacker selects a path of highest non-detection probability on a network with multiple origins and multiple available targets. A defender allocates a limited number of resources within the geographic region of the network to reduce the maximum network non-detection probability between all origin-target pairs by reducing arc non-detection probabilities and where path non-detection probability is modeled as a product of all arc non-detection probabilities on that path. Traditional decomposition methods to solve the shortest path network interdiction problem are sensitive to problem size and network/regional complexity. The goal of this paper is to develop a method for approximating the regional allocation of defense resources that maintains accuracy while reducing both computational effort and the sensitivity of computation time to network/regional properties. Statistical and spatial analysis methods are utilized to verify approximation performance of the knapsack method in two real-world networks.     

Fast massively parallel algorithms for shortest path within planar figures

s and t within a given planar figure F is considered. The approach contains basic methodology developed for any parallel or distributed system. The 2D scene or the edge of F are represented in the n Cartesian coordinate system (n-CCS). Several algorithms for the shortest path are given, each one to be applied in specified circumstances depending on the exact machine model or on additional information concerning geometrical properties of the figure. If these algorithms are implemented in a parallel depth search machine (PDSM), then the shortest path can be computed in time O(1). The maximum number of processors used is 0(n). The given methodology can also be adapted for producing an approximate solution when the shortest path is approximated by polygonal lines.     

最短路径在分布式资源目录中的应用

为了实现对海量多源数据资源的统一管理和资源共享,满足分布数据存储环境下对数据的统一管理和高效检索要求;利用LDAP (lightweight directory access protocol)轻量级目录服务访问协议进行设计并实现了分布式资源目录系统结构,并在此基础上针对服务器间查询速率低的问题提出了应用最短路径算法提高查询速率的方法.实验结果表明,利用LDAP协议实现了分布式资源目录的存储及管理,应用最短路径算法能够显著提高分布式资源目录的查询效率.     

A shortest augmenting path algorithm for dense and sparse linear assignment problems

We develop a shortest augmenting path algorithm for the linear assignment problem. It contains new initialization routines and a special implementation of Dijkstra's shortest path method. For both dense and sparse problems computational experiments show this algorithm to be uniformly faster than the best algorithms from the literature. A Pascal implementation is presented.     

物流配送最短路径网搜索的改进蚁群算法

将蚁群优化的基本原理用到物流配送网最短路径搜索中,在充分考虑了物流配送网基本特性后,采用了一种基于加强方向性搜索、减少搜索范围的蚁群算法对其进行具体实现.改进的蚁群算法改善了基本蚁群算法中的随机搜索特性,使算法能以较快的速度收敛到最优解上.     

An iterative stochastic algorithm based on distributed learning automata for finding the stochastic shortest path in stochastic graphs

The Journal of Supercomputing - In this paper, we study the problem of finding the shortest path in stochastic graphs and propose an iterative algorithm for solving it. This algorithm is based on...     

An efficient fault-containing self-stabilizing algorithm for the shortest path problem

Shortest path finding has a variety of applications in transportation and communication. In this paper, we propose a fault-containing self-stabilizing algorithm for the shortest path problem in a distributed system. The improvement made by the proposed algorithm in stabilization times for single-fault situations can demonstrate the desirability of an efficient fault-containing self-stabilizing algorithm. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), where Δ is the maximum node degree in the system, and the contamination number of the proposed algorithm is 1.     

Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment

A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method.     

A genetic algorithm for shortest path routing problem and the sizing of populations

This paper presents a genetic algorithmic approach to the shortest path (SP) routing problem. Variable-length chromosomes (strings) and their genes (parameters) have been used for encoding the problem. The crossover operation exchanges partial chromosomes (partial routes) at positionally independent crossing sites and the mutation operation maintains the genetic diversity of the population. The proposed algorithm can cure all the infeasible chromosomes with a simple repair function. Crossover and mutation together provide a search capability that results in improved quality of solution and enhanced rate of convergence. This paper also develops a population-sizing equation that facilitates a solution with desired quality. It is based on the gambler ruin model; the equation has been further enhanced and generalized. The equation relates the size of the population, quality of solution, cardinality of the alphabet, and other parameters of the proposed algorithm. Computer simulations show that the proposed algorithm exhibits a much better quality of solution (route optimality) and a much higher rate of convergence than other algorithms. The results are relatively independent of problem types for almost all source-destination pairs. Furthermore, simulation studies emphasize the usefulness of the population-sizing equation. The equation scales to larger networks. It is felt that it can be used for determining an adequate population size in the SP routing problem.