随机时间依赖网络的K期望最短路径

首先给出了随机时间依赖网络模型，K期望是短路径问题的形式化描述，并针对公交网络推导出到达弧头结点的时刻所服从的概率密度函数，路径期望耗费的计算方法，然后，基于随机一致性假设和胡机优势的概念给出了K期望最短路径问题的理论基础和算法并证明了算法的正确性，最后，给出了公交网络的应用实例和实验结果。     

Finding Reliable Shortest Paths in Road Networks Under Uncertainty

The aim of this study is to investigate the solution algorithm for solving the problem of determining reliable shortest paths in road networks with stochastic travel times. The availability of reliable shortest paths enables travelers, in the face of travel time uncertainty, to plan their trips with a pre-specified on-time arrival probability. In this study, the reliable shortest path between origin and destination nodes is determined using a multiple-criteria shortest path approach when link travel times follow normal distributions. The dominance conditions involved in such problems are established, thereby reducing the number of generated non-dominated paths during the search processes. Two solution algorithms, multi-criteria label-setting and A* algorithms, are proposed and their complexities analyzed. Computational results using large scale networks are presented. Numerical examples using data from a real-world advanced traveller information system is also given to illustrate the applicability of the solution algorithms in practice.     

Õ(Congestion + Dilation) Hot-Potato Routing on Leveled Networks

We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For store-and-forward routing, in which nodes have buffers for packets in transit, there are routing algorithms with a performance that matches the lower bound Ω(C+D). Motivated from optical networks, we study hot-potato routing in which the nodes are bufferless. Due to the lack of buffers, in hot-potato routing the packets may be delayed more than in store-and-forward routing. An interesting question is how much is the performance of routing algorithms affected by the absence of buffers. Here, we answer this question for the class of leveled networks, in which the nodes are partitioned into L+1 distinct levels. We present a randomized hot-potato routing algorithm for leveled networks, which routes the packets in O((C + L) ln⁹ (LN)) time with high probability. For routing problems with dilation Ω(L), and where N is a polynonial in L, this bound is within polylogarithmic factors of the lower bound Ω(C+L). Our algorithm demonstrates that for such routing problems the benefit from using buffers is no more than polylogarithmic; thus, hot-potato routing is an efficient way to route packets in leveled networks. In hot-potato routing, due to the lack of buffers, the packets may not be able to remain on their preselected paths during the course of routing (while in store-and-forward routing the packets remain on their preselected paths). However, in our algorithm the actual path that each packet follows contains its original preselected path; thus the lower bound Ω(C+L) is also a lower bound for the new paths. Our algorithm is distributed, that is, routing decisions are taken locally at each node while packets are routed in the network. To our knowledge, this is the first hot-potato algorithm designed and analyzed, in terms of congestion and dilation, for leveled networks.     

Mesh网络路由算法容错性的概率分析

该文基于k-Mesh子网的概念提出了两个简单的基于局部信息和分布式的Mesh网络容错路由算法，并对其容错性进行概率分析；在每个结点具有独立的出错概率的假设条件下，推导出路由算法成功返回由正确结点组成的路径的概率．该文运用严格的数学推理，证明了Mesh网络结点出错概率只要控制在1．87％以内，则对于多达几十万个结点的Mesh网络，提出的路由算法具有99％的概率确保找到正确结点组成的路径．路由算法的时间复杂性是线性的．模拟结果表明路由算法所构造的路由路径长度非常接近于两结点之间的最优路径长度．     

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。     

Hyperpath-based vehicle routing and scheduling method in time-varying networks for airport shuttle service

It is very significant for a reasonable vehicle routing and scheduling in city airport shuttle service to decrease operational costs and increase passenger satisfaction. Most of the existing reports for such problems assumed that the travel time was invariable. However, the ever-increasing traffic congestion often makes it variable. In this study, considering the time-varying networks, a vehicle routing and scheduling method is proposed, where the time-varying feature enables the traveler to select a direction among all the Pareto-optimal paths at each node in response to the knowledge of the time window demands. Such Pareto-optimal paths are referred to hyperpaths herein. To obtain the hyperpaths, an exact algorithm is designed in this study for addressing the bi-criteria shortest paths problem, where the travel time comes to be discontinuous time-varying. Given the techniques that generate all Pareto-optimal solutions exhibiting exponential worst-case computational complexity, embedded in the exact algorithm, a computationally efficient bound strategy is reported on the basis of passenger locations, pickup time windows and arrival time windows. As such, the vehicle routing and scheduling problem viewed as an arc selection model can be solved by a proposed heuristic algorithm combined with a dynamic programming method. A series of experiments by using the practical pickup data indicate that the proposed methods can obtain cost-saving schedules under the condition of time-varying travel times.

     

Finding the Most Reliable Strategy on Stochastic and Time-Dependent Transportation Networks: A Hypergraph Based Formulation

This study addresses the problem of determining the most reliable time-adaptive strategy on a stochastic and time-dependent transportation network. The reliability is measured as a conic combination of the mean and standard-deviation of travel time and is termed robust-cost. The stochastic time-dependent network is represented as a directed acyclic hypergraph, where the time-adaptive strategies correspond to the hyperpaths. This representation transforms the problem to that of determining the hyperpath with the least robust-cost on the constructed hypergraph. The minimum robust-cost strategy problem is difficult to solve because of the non-linear objective function. Consequently, the solution procedures commonly adopted in the literature —that are based on substrategy optimality and substrategy non-dominance —are not applicable to this problem. In this light, we propose a novel bounds-based iterative algorithm that determines the minimum robust-cost strategy on the stochastic and time-dependent networks. This algorithm needs to determine the least and K-best strategies in the second moment of travel time, for which an efficient procedure is also proposed. The algorithm is shown to be exact and exhibit parameterically polynomial behavior; computational tests were performed to demonstrate its efficiency. Further, tests showed that the minimum robust-cost strategy compromises little in terms of the mean travel time (0.2%–2.9%) —compared to least expected travel time strategy— with significant reduction in travel time variability (6.2%–29.8%).     

传感器网络定向扩散机制中梯度生成算法的研究

如何生成优化的梯度是传感器网络定向扩散中的一个关键问题,本文在分析一种基本梯度生成算法的问题基础之上,利用兴趣包的转发次数对其进行改进,设计了一种分布式的最短路径梯度生成算法.该算法极大的降低了邻居节点间建立"平行梯度"和"逆向梯度"的概率,可构建从源节点到sink节点的多条最短路径.仿真表明,改进的算法可建立更为有效的梯度,从而使得定向扩散中数据报文沿着更短的路径传输,无线传感器网络的能量利用率更高.     

Fast approximation of betweenness centrality through sampling

Betweenness centrality is a fundamental measure in social network analysis, expressing the importance or influence of individual vertices (or edges) in a network in terms of the fraction of shortest paths that pass through them. Since exact computation in large networks is prohibitively expensive, we present two efficient randomized algorithms for betweenness estimation. The algorithms are based on random sampling of shortest paths and offer probabilistic guarantees on the quality of the approximation. The first algorithm estimates the betweenness of all vertices (or edges): all approximate values are within an additive factor \(\varepsilon \in (0,1)\) from the real values, with probability at least \(1-\delta \). The second algorithm focuses on the top-K vertices (or edges) with highest betweenness and estimate their betweenness value to within a multiplicative factor \(\varepsilon \), with probability at least \(1-\delta \). This is the first algorithm that can compute such approximation for the top-K vertices (or edges). By proving upper and lower bounds to the VC-dimension of a range set associated with the problem at hand, we can bound the sample size needed to achieve the desired approximations. We obtain sample sizes that are independent from the number of vertices in the network and only depend on a characteristic quantity that we call the vertex-diameter, that is the maximum number of vertices in a shortest path. In some cases, the sample size is completely independent from any quantitative property of the graph. An extensive experimental evaluation on real and artificial networks shows that our algorithms are significantly faster and much more scalable as the number of vertices grows than other algorithms with similar approximation guarantees.     

Multicriteria Stochastic Shortest Path Problem for Electric Vehicles

This paper formulates the reliable routing of electric vehicles in stochastic networks as a multicriteria shortest path problem with travel time and charging cost components. The reliability term is defined as the probability of finishing the trip without running out of charge. The arc travel times are represented as stochastic variables, and arc energy consumption is modeled as a linear function of arc length and arc travel time. The traveler aims to minimize the generalized cost, formulated as a linear function of travel time and charging cost, subject to a minimum reliability threshold, representing the level of risk a traveler is willing to take in favor of routes with lower cost. We propose a solution algorithm based on generalized dynamic programming and show that the optimal solution may include cycles that visit at least one charging station. The properties of the proposed multicriteria shortest path problem are mathematically proved. The simulation results on randomly-generated networks show that cyclic paths are very rare, and that the generalized cost of travel is a monotone increasing function of minimum reliability threshold.     

Shortest distance and reliability of probabilistic networks

When the “length” of a link is not deterministic and is governed by a stochastic process, the “shortest” path between two points in the network is not necessarily always composed of the same links and depends on the state of the network. For example, in communication and transportation networks, the travel time on a link is not deterministic and the fastest path between two points is not fixed. This paper presents an algorithm to compute the expected shortest travel time between two nodes in the network when the travel time on each link has a given independent discrete probability distribution. The algorithm assumes the knowledge of all the paths between two nodes and methods to determine the paths are referenced.In reliability (i.e. the probability that two given points are connected by a path) computations, associated with each link is a probability of “failure” and a probability of “success”. Since “failure” implies infinite travel time, the algorithm simultaneously computes reliability. The paper also discusses the algorithm's capability to simultaneously compute some other performance measures which are useful in the analysis of emergency services operating on a network.     

Multi-objective α-reliable path finding in stochastic networks with correlated link costs: A simulation-based multi-objective genetic algorithm approach (SMOGA)

In this study, we propose a new simulation-based multi-objective genetic algorithm (SMOGA) approach to find a portfolio of reliable nondominant (Pareto) paths, a set of paths that is equally good or better at least in one objective space compared to all other paths, in stochastic networks while considering link travel time uncertainties and correlations among link travel times. Our SMOGA model consists of a Monte Carlo simulation, a genetic algorithm, and a Pareto filter module to find a set of Pareto paths that minimize the travel time budgets required to satisfy multiple requirements of travel time reliability pre-determined by users. For our purposes, an alpha (and beta) reliable path finding problem is first formulated as a variant of Chance Constrained Multi-objective Programming (CCMOP) model. Then the simulation module is used to simulate stochastic networks with correlations among link travel times, and genetic algorithm and Pareto filter module are used to effectively search for Pareto paths that satisfy multiple reliability requirements in combinatorial solution space. Numerical results on the Chicago Sketch network demonstrate that our carefully designed genetic representation (a variable-length chromosome and two ways of generating initial population) and genetic operators (a crossover and a mutation operator) effectively explore solution space and ensure the feasibility and diversity of offspring paths. Further, our graphical representations of Pareto paths on the same network indicate that simplified models that do not consider correlations among link travel time distributions may find Pareto paths with a significant bias in travel time budgets and hence provide travelers sub-optimal paths.     

On the sum-max bicriterion path problem

In network analysis, there are many applications in which several weights associated with traversing each arc are given, so it is natural to consider multiple-objective path problems. Usually, there is no path which is simultaneously optimal with respect to all objective functions, so it will be necessary to obtain efficient paths of interest, i.e. paths for which there exists no other path that yields an improvement in one of the objective functions without causing a degradation in the others. Methods for determining efficient paths form part of a very extensive literature on multiple-objective optimization, most of them being proposed for objectives defined by sum functions. Our aim is to study the particular case of a bicriterion problem whose objective functions are defined by a sum and a maximum. A very important aspect of this problem is to find a best compromise solution, which is shown to be equivalent to solve the quickest path problem, which has interesting applications in communication and transportation networks.In this paper, we study a special class of bicriterion path problems where the objective functions are defined by a sum and a maximum: The sum-max bicriterion path problem (SMBPP). After reviewing some special kinds of efficient paths, we propose some algorithms to generate these kinds of efficient paths, based on a progressive reduction of the original network. We analyse its relationship with the quickest path problem (QPP), showing that this is equivalent to the weighted problem associated to the SMBPP, which is also solved by a modification of an algorithm proposed for the QPP. A computational study is presented which shows the superiority of the algorithm proposed in this paper over other existing algorithms to generate the entire set E of efficient paths of the SMBPP.     

Transmission reliability of k minimal paths within time threshold

The quickest path problem involving two attributes, the capacity and the lead time, is to find a single path with minimum transmission time. The capacity of each arc is assumed to be deterministic in this problem. However, in many practical networks such as computer networks, telecommunication networks, and logistics networks, each arc is multistate due to failure, maintenance, etc. Such a network is named a multistate flow network. Hence, both the transmission time to deliver data through a minimal path and the minimum transmission time through a multistate flow network are not fixed. In order to reduce the transmission time, the data can be transmitted through k minimal paths simultaneously. The purpose of this paper is to evaluate the probability that d units of data can be transmitted through k minimal paths within time threshold T. Such a probability is called the transmission reliability. A simple algorithm is proposed to generate all lower boundary points for (d, T), the minimal system states satisfying the demand within time threshold. The transmission reliability can be subsequently computed in terms of such points. Another algorithm is further proposed to find the optimal combination of k minimal paths with highest transmission reliability.     

Realizing and benchmarking broadcast algorithms in wireless mesh networks

Broadcasting by flooding causes the broadcast storm problem in multi-hop wireless networks. This problem becomes more likely in a wireless mesh network (WMN) because WMNs can bridge wired LANs, increasing broadcast traffic and collision probability. Since the network control, routing, and topology maintenance of a WMN highly rely on layer-2 broadcasting, unreliable broadcast algorithms directly destabilize a WMN. Researchers have developed many algorithms for efficient and reliable broadcast in multi-hop wireless networks. However, real-world systems rarely verify or compare these approaches, especially in a WMN. This paper examines six representative broadcast algorithms: simple flooding, dynamic probabilistic, efficient counter-based broadcast, scalable broadcast, domain pruning, and connected-dominating-set based algorithms. This study addresses both common and algorithm-specific implementation in a real-world IEEE 802.11s WMN testbed. Experiments under various topologies and packet lengths reveal the reliability, forwarding ratio, and efficiency of these six algorithms. Quantitative survey results indicate that the scalable broadcast algorithm possesses the best reliability due to its lower collision probability. The domain-pruning algorithm is the most efficient algorithm when considering both reliability and the forwarding ratio.     

Backup path set selection in ad hoc wireless network using link expiration time

Topological changes in mobile ad hoc networks frequently render routing paths unusable. Such recurrent path failures have detrimental effects on quality of service. A suitable technique for eliminating this problem is to use multiple backup paths between the source and the destination in the network. Most of the proposed on-demand routing protocols however, build and rely on single route for each data session. Whenever there is a link disconnection on the active route, the routing protocol must perform a path recovery process. This paper proposes an effective and efficient protocol for backup and disjoint path set in an ad hoc wireless network. This protocol converges into a highly reliable path set very fast with no message exchange overhead. The paths selection according to this algorithm is beneficial for mobile ad hoc networks, since it produces a set of backup paths with much higher reliability. Simulations are conducted to evaluate the performance of our algorithm in terms of route numbers in the path set and its reliability. In order to acquire link reliability estimates, we use link expiration time (LET) between each two nodes.In another experiment, we save the LET of entire links in the ad hoc network during a specific time period, then use them as a data base for predicting the probability of proper operation of links.Links reliability obtains from LET. Prediction is done by using a multi-layer perceptron (MLP) network which is trained with error back-propagation error algorithm. Experimental results show that the MLP net can be a good choice to predict the reliability of the links between the mobile nodes with more accuracy.     

复杂社会网络的介数性质近似计算方法研究

随着计算机和互联网的迅猛发展,面向互联网的社会网络挖掘和分析成为一个新的课题。从互联网挖掘的社会网络往往规模巨大,这对网络分析算法的性能提出了更高的要求 。介数值作为图的重要结构性质,广泛应用于基于图的聚类、分类算法,如何降低其计算的复杂性是急需解决的问题。目前,常用的方法是利用对最短路径长度的近似来降低低网络分析算法的复杂性,但已有的近似方法没有考虑现实大规模网络的复杂网络特性,对最短路径长度的近似方 近似计算方法,其基本思想是结合复杂网络的结构特性,利用通过网络中枢节点的路径来近似最短路径,以近似的最短路径求得介数的近似值。这为图的结构性质的近似估算算提供了一种新颖的思路。通过与传统的介数计算方法和近的分析得到了若干有益的结论,为进一步的研究工作奠定了基础。     

Optimal paths in probabilistic networks: A case with temporary preferences

The classical shortest route problem in networks assumes deterministic arc weights and a utility (or cost) function that is linear over path weights for route evaluation. When the environment is stochastic and the “traveler's” utility function for travel attributes is nonlinear, we define “optimal paths” that maximize the expected utility.We review the concepts of temporary and permanent preferences for comparing a traveler's preference for available subpaths. It has been shown before that when the utility function is linear or exponential, permanent preferences prevail and an efficient Dijkstra-type algorithm [3] is available that determines the optimal path.In this paper an exact procedure is developed for determining an optimal path when the utility function is quadratic—a case where permanent preferences do not always prevail. The algorithm uses subpath comparison rules to establish permanent preferences, when possible, among subpaths of the given network. Although in the worst case the algorithm implicitly enumerates all paths (the number of operations increasing exponentially with the size of the network), we find, from the computational experience reported, that the number of potentially optimal paths to evaluate is generally manageable.     

Approximate distributed top-<Emphasis Type="Italic">k</Emphasis> queries

We consider a distributed system where each node keeps a local count for items (similar to elections where nodes are ballot boxes and items are candidates). A top-k query in such a system asks which are the k items whose global count, across all nodes in the system, is the largest. In this paper, we present a Monte Carlo algorithm that outputs, with high probability, a set of k candidates which approximates the top-k items. The algorithm is motivated by sensor networks in that it focuses on reducing the individual communication complexity. In contrast to previous algorithms, the communication complexity depends only on the global scores and not on the partition of scores among nodes. If the number of nodes is large, our algorithm dramatically reduces the communication complexity when compared with deterministic algorithms. We show that the complexity of our algorithm is close to a lower bound on the cell-probe complexity of any non-interactive top-k approximation algorithm. We show that for some natural global distributions (such as the Geometric or Zipf distributions), our algorithm needs only polylogarithmic number of communication bits per node. An extended abstract of this paper appeared in Proc. 13th Int. Colloquium on Structural Information and Communication Complexity, SIROCCO 2006, Lecture Notes in Computer Science 4056, pp. 319–333.     

最小时间路径算法的改进及在路径优化中的应用*

由于城市交通网络中路径行程时间是随着时间的变化而变化的,求解最小时间路径比较困难,为此提出把交通网络抽象为时间依赖的网络模型的解决方法。对时间依赖网络模型和理论基础进行分析,指出文献［1］描述的最小时间路径算法存在的不足,即不能正确记录路径;通过引入一个记录路径的数组来对此算法进行改进,改进后的算法不仅解决了原算法存在的问题,而且可以满足n∶1的最短路径搜索,扩展了原算法的应用范围。最后用实验验证了改进算法的正确性和有效性。