迷宫最短路径问题新算法

提出了求解迷宫最短路径问题的新算法,该算法抛弃了经典算法(深度优先搜索和广度优先搜索)中繁杂低效的递归、回溯思想。通过合理的变换,将原问题转化为迷宫路径深度图的生成问题。最后对算法进行了严谨的分析和实例测试,显示出该算法易于理解、易于编程、时间空间复杂度低等优点。     

改进Dijkstra算法在GIS导航应用中最短路径搜索研究

研究GIS在电子导航系统应用中的最短路径搜索效率问题。在电子导航系统中对最短路径的搜索效率要求很高。随着城市发展交通线路剧增,传统的基于Dijkstra算法的GIS导航系统不能适应日益复杂的交通线路,存在最短路径搜索效率过低的问题。考虑到GIS空间分布的特性,提出了改进的Dijkstra算法用以解决GIS导航中的最短路径搜索问题。改进算法不仅避免了传统Dijkstra算法逐个节点遍历搜索,而且根据方向优先特性缩小搜索范围,大大减少了搜索工作量,并通过改变搜索节点存储的数据结构提高了最短路径的搜索效率。实验表明,这种改进算法较之传统算法能够有效提高最短路径的搜索效率,满足了电子导航系统对最短路径搜索效率的要求,取得了满意的结果。     

国际航线网络中K条最短路径算法改进与仿真

K条最短路径(KSP)问题是国际航线网络实际路径优化问题。通过对航线网络特征与K条最短路径算法的分析,研究了解决KSP问题的典型Yen算法。针对Yen算法求解候选路径占用大量运算时间的问题,提出一种改进Yen算法。改进Yen算法通过借助A*算法的启发式策略,减少了产生候选航线路径的时间,从而提高了算法的搜索效率并减小了算法搜索的规模。通过对国际航线网络实例的仿真,实验结果表明改进Yen算法能够快速求解国际航线网络中的KSP问题;同时,与Yen算法相比,运算效率提升了75.19%以上,能够为航线路径优化提供决策支持。     

公交车网络的最短路径算法及实现

最短路径问题是图论研究中的一个经典算法问题．旨在寻找图中任意两结点之间的最短路径。一般在交通道路网络中最短路径问题就是单纯地求解两点问的最短路径。为了保证实用性，公交车网络的最短路径算法以转车次数最少为首要目的。文中借鉴广度优先搜索的思路来求解最短路径，即逐个找出经过起点站和终点站的车次以及这些车次沿途可转的车次。首先说明了算法的计算机实现方法，再举例详细说明其过程，最后指出此算法的扩充用途。     

公交车网络的最短路径算法及实现

最短路径问题是图论研究中的一个经典算法问题,旨在寻找图中任意两结点之间的最短路径.一般在交通道路网络中最短路径问题就是单纯地求解两点间的最短路径.为了保证实用性,公交车网络的最短路径算法以转车次数最少为首要目的.文中借鉴广度优先搜索的思路来求解最短路径,即逐个找出经过起点站和终点站的车次以及这些车次沿途可转的车次.首先说明了算法的计算机实现方法,再举例详细说明其过程,最后指出此算法的扩充用途.     

基于优先队列的时变网络最短路径算法

提出了基于优先队列的时变网络最短路径算法,能克服传统最短路径算法难以对时变网络求解最短路径的缺陷。提出的时间窗选择策略能够在算法求解过程中为节点选择合适的时间窗以降低路径长度,从而求得精确解。进一步地,算法使用了优先队列组织节点集合以提高计算效率。在随机生成的网络数据以及美国道路数据上的实验表明,基于优先队列的时变网络最短路径算法与经典方法相比,不仅能够求得精确解,运算速度也有所提高。     

一种基于路径阻断的求解最短路径算法

全源最短路径的求解是计算机科学、交通工程、地理信息系统等学科中的一个研究热点。随着网络规模不断增大,求解全源最短路径的时间复杂度急剧上升,这制约了复杂网络相关研究与应用的快速发展,因此最短路径算法的效率问题是普遍关注并且在实际应用中迫切需要解决的问题。本文在BFS的基础上,引入路径阻断策略,利用已求得的单源最短路径节点的结果,加速全源最短路径的求解。实验结果表明该方法对大规模网络全源最短路径实现了加速计算。     

一种SRIO网络负载均衡最短路径路由算法

在串行RapidIO传输过程中,路由选路算法是影响传输性能的重要因素之一。针对串行高速输入-输出(SRIO)网络深度优先搜索分配路径非最优问题,提出一种负载均衡最短路径路由算法。通过广度优先搜索对SRIO网络中的节点进行枚举并建立网络拓扑信息,以路由跳数定义路由的成本,根据改进Floyd-WarShall算法计算并保存交换节点间的K最短路径。给出预期负载的概念和链路上的路由路径数量来定义链路的负载,采用负载均衡算法从K最短路径中进行选路,建立SRIO网络最短路径约束的负载均衡路由。实验结果表明,与深度遍历路由算法、最小跳数算法相比,该算法在网络传输平均跳数、链路平均负载和链路负载均衡方面有更好的表现,能够有效提升SRIO路由网络的稳定性。     

基于Dijkstra最短路径算法研究

Dijkstra算法是经典的求解单源静态最短路径问题的理论基础,但是在实际应用中存在一些不足之处,影响了算法的效率.本文首先介绍了Dijkstra算法,分析了该算法的优点与缺点,并在此基础上提出求解最短路径在数据存储和搜索上的一种改进算法.     

过必经节点集的动态剪枝搜索算法

针对过必经节点集的最短路径问题,提出一种基于动态减枝策略的深度优先搜索算法（Depth First Search based on Dynamic Pruning,DP-DFS）,该算法构建一个二维矩阵,每搜索一个节点,比较当前路径的权值和与矩阵中已保存的权值,如果当前路径的权值小于矩阵中保存的权值,则更新矩阵中权值为当前较小的路径权值,否则进行剪枝。该算法比较适合较大规模的图搜索,实验表明,必经节点个数在50以内时,利用该算法可以在30?s内找到一条近似最优的最短路径。     

Novel route maintenance protocols for the Bluetooth ad hoc network with mobility

Bluetooth technology is specially designed for the wireless personal area networks to replace cable. Several challenges exist in Bluetooth scatternet formation and routing, since nodes can arrive and depart at arbitrary times. In this paper, novel route maintenance algorithms are proposed for the Bluetooth ad hoc networks, where nodes can enter or exit from the piconets time to time. Our protocols guarantee the connectivity among nodes and reconstruct the routes dynamically by considering location information of the nodes. Besides, it is proposed how to reduce the number of hops and to form the shortest route between the source and the destination due to addition of new nodes to a piconet. Performance analysis of our protocols show that they outperform in terms of end to end transmission delay, bandwidth consumption and average hop counts as compared to similar Bluetooth routing protocols that we have considered.     

双环网络[+1]边优先最短路径及其寻径策略

双环网络是一种非常重要的互联网络结构 .传统的最优寻径方法没有充分利用这一网络中同一节点到不同节点的最短路径之间的关系 ,所给的算法不是最优的 .定义了双环网络的一种最短路径—— [+ 1]边优先最短路径 ,在此形式下 ,不仅最短路径的形式唯一而且同一源节点到不同目的节点的最短路径之间存在递推关系 .给出了相应的递推公式 ,运用此公式 ,平均不到两次加法运算和一次比较即可找到源节点到所有其它节点的最短路径 .利用所得结果 ,源节点只需存储很少的信息就可以通过简单计算求得到任意其它节点的最短路径 .与传统方法相比 ,本算法提高了系统的寻径效率     

对无线传感器网络区域数据聚合有效性的研究

通过抽象出无线传感器网络中区域数据回传的网络模型，定量研究了区域数据聚合的节能条件，证明了先聚合再回传比直接进行数据回传所节省的相对路径长度,如果大于等于数据相关性与源节点个数的比值时，区域数据聚合一定可以节省能耗，并进一步给出了当数据聚合点在网络的不同位置，或数据的空间相关性不同时，区域数据聚合的节能条件。对于无线传感器网络的部署、路由协议的选择及评估数据聚合算法的能量有效性等，均具有一定的参考价值。     

Finding the shortest path in stochastic networks

Common network parameters, such as number of nodes and arc lengths are frequently subjected to ambiguity as a result of probability law. A number of authors have discussed the calculation of the shortest path in networks with random variable arc lengths. Generally, only a subset of intermediate nodes chosen in accordance with a given probability law can be used to transition from source node to sink node. The determination of a priori path of the minimal length in an incomplete network is defined as a probabilistic shortest path problem. When arc lengths between nodes are randomly assigned variables in an incomplete network the resulting network is known as an incomplete stochastic network. In this paper, the computation of minimal length in incomplete stochastic networks, when travel times between nodes are allowed to be exponentially distributed random variables, is formulated as a linear programming problem. A practical application of the methodology is demonstrated and the results and process compared to the Kulkarni’s [V.G. Kulkarni, Shortest paths in networks with exponentially distributed arc lengths, Networks 16 (1986) 255–274] method.     

Travelling time on dense networks

The earliest arrival time and the minimal travelling time from source to destination are not, in general, the same. In fact they are different for a wide class of networks. The first is measured from the time one is ready to leave the source until his arrival at the destination. The second is measured only from the actual departure time from the source. Various forms of the earliest arrival problem, or equivalenlly the shortest route problem, have been studied: requirements for visiting specified nodes, penalties on turns, time-dependent lengths of arcs, and others. In this paper we discuss the case where some edges are closed for travelling during specified periods of time. Parking is permitted at the vertices of the network when it is necessary to wait for an arc to be opened, but we also assume the possibility of “no-parking” or “occupied” periods in the nodes.Given such restrictions on movement and parking in the network, travelling time may sometimes be shortened at the expense of later arrival time. The paper presents an algorithm for the solution of the minimal travelling problem. With a minor change this algorithm also solves the earliest arrival problem.     

Reconstruction of graphs based on random walks

The analysis of complex networks is of major interest in various fields of science. In many applications we face the challenge that the exact topology of a network is unknown but we are instead given information about distances within this network. The theoretical approaches to this problem have so far been focusing on the reconstruction of graphs from shortest path distance matrices. Often, however, movements in networks do not follow shortest paths but occur in a random fashion. In these cases an appropriate distance measure can be defined as the mean length of a random walk between two nodes — a quantity known as the mean first hitting time.In this contribution we investigate whether a graph can be reconstructed from its mean first hitting time matrix and put forward an algorithm for solving this problem. A heuristic method to reduce the computational effort is described and analyzed. In the case of trees we can even give an algorithm for reconstructing graphs from incomplete random walk distance matrices.     

Broadcasting on Incomplete WK-Recursive Networks

The WK-recursive networks, which were originally proposed by Vecchia and Sanges, have suffered from a rigorous restriction on the number of nodes. Like other incomplete networks, the incomplete WK-recursive networks have been proposed to relieve this restriction. In this paper, broadcasting on the incomplete WK-recursive networks is discussed. The proposed broadcasting algorithm is optimal with respect to message complexity. Besides, extensive experiments are made to evaluate its performance. Experimental results show that (1) the heights of the broadcasting trees do not exceed the diameters, (2) a high percentage of the nodes can receive the message from the source node via the shortest paths, (3) for those nonshortest transmission paths, the deviations are small, and (4) a high percentage of the broadcasting trees are of minimum height.     

稳定的最短路径树及其构造算法

构建最短路径树是动态网络研究的重要问题之一。在动态网络中,当边状态发生变化时会引发最短路径树动态的重新构建,反复地计算不仅消耗大量时间,也会导致最短路径树的频繁变化。提出一种稳定的最短路径树构造算法,使得构造的路径树在动态网络上更稳定,即更新最短路径树所需的操作数更少。该算法通过记录频繁变化的不稳定边并尽可能避免将其加入最短路径树中,从而能够高效地减少边变化带来的操作。实验结果表明,与传统的动态最短路径树算法相比,该算法可以得到更稳定的最短路径树,并且更新时间减少了57.24%,结点更新次数降低了43.6%。     

New polynomial time algorithms to compute a set of Pareto optimal paths for multi-objective shortest path problems

Multi-objective shortest path problem (MOSPP) is an active area of research because of its application in a large number of systems such as transportation systems, communication systems, power transmission systems, pipeline distribution systems of water, gas, blood and drainage, neural decision systems, production planning and project planning. In these networks it becomes necessary to find the best path from one node to a specified or all other nodes. The computational complexity of the existing algorithms in the literature to compute all Pareto minimum paths from a specified source node to all other nodes in an MOSPP is of exponential order in the worst case. Instead of generating all the values of the Pareto minimum paths in exponential time, we propose an algorithm to find a set of values of the Pareto minimum paths in polynomial time, which is very significant in many contexts. If an MOSPP of a network is having negative cycle, all the existing algorithm only indicate the existence of the negative cycle, that too after exponential number of operations. However, applying the proposed algorithm, we can find a set of Pareto minimum paths of any MOSPP of a network even if it contains negative cycles. The proposed algorithm is illustrated with examples.     

Simulation modeling and analysis of the hop count distribution in cognitive radio ad-hoc networks with shadow fading

The number of hops between source node and destination node is a key parameter in studying multi-hop wireless networks. Although hop count in wireless ad-hoc networks (AHNs) has been studied in the literature, no works on investigating the hop count characteristics in cognitive environments have been carried out. In this paper, we model cognitive radio ad-hoc networks (CRAHNs) as geometric random graphs and then propose a framework for studying the hop count distribution and correlated connectivity of communication path between two arbitrary nodes in CRAHNs with shadow fading. The framework consists of an algorithm and a methodology. Specifically, from the perspective of geometric random graph, the algorithm finds all possible paths between two arbitrary nodes and returns the hop count of the shortest path between them by using the global location information of nodes, i.e. primary users – PUs and secondary users – SUs, and the active states of PUs as input data. Meanwhile, through huge number of random network topology trials, the methodology returns the hop count distribution and connection status of communication path between two arbitrary nodes in CRAHNs with shadow fading. From the evaluating scenarios in this paper, important features of hop count distribution and connectivity and their correlating relationship in CRAHNs with shadow fading are revealed and compared with those in AHNs and in CRAHNs without shadow fading.