Calcul des métriques de routage pour Internet

In spite of the development of Internet networks and the important volume of literature dealing with Internet routing, many fundamental topics were not addressed. Traffic is, in principle, routed through shortest paths, in sense of a set of link weights (a metric). These weights do not necessarily have a physical significance and could be modified by the network administrator to change the routing policy and the network cost. In this paper, we give precise answers for the following questions: 1/ Given a network topology, is there a metric such that, first, the shortest path between any pair of vertices is unique and, second, every link belongs to at least one shortest path ? 2/ How can we compute such a metric ? 3/ Can we choose a metric satisfying these constraints and whose values are small integers ? 4/ If the routers of the network have differents functions and caracteristics, is it possibe to determine a metric which allows to route traffic, taking into account these heteregeneous caracteristics ? 5/ If some routing paths are seleceted due to technical or economical reasons, can we find a metric enforcing this given routing policy ? 6/ If this is not possible, what should we do to compute a metric that is as close as possible to the selected routing paths ?     

Designing reliable networks with short paths

We present a technique for constructing highly reliable networks in which locations consist of pairs of redundant vertices and in which every pair of locations has a pair of short disjoint paths connecting them. One of the paths between locations has one hop and, in most cases, the other path between locations has two hops. We further show that the networks have as few edges as possible and the vertices in the networks have nearly as small a degree as possible.     

用最短路径法选择布线路径

本文对详细布线介绍一种用最短路径的方法选择布线路径,重点提出了几条启发式的布线原则和函数表达式。通过组建一张带权有向图,然后用最短路径算法获得布线解。本文的方法巳在DDCR四边布线器中用C语言实现。     

The stable paths problem and interdomain routing

Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem since any interdomain protocol is required to allow policy-based metrics to override distance-based metrics and enable autonomous systems to independently define their routing policies with little or no global coordination. It is then natural to ask if BGP can be viewed as a distributed algorithm for solving some fundamental problem. We introduce the stable paths problem and show that BGP can be viewed as a distributed algorithm for solving this problem. Unlike a shortest path tree, such a solution does not represent a global optimum, but rather an equilibrium point in which each node is assigned its local optimum. We study the stable paths problem using a derived structure called a dispute wheel, representing conflicting routing policies at various nodes. We show that if no dispute wheel can be constructed, then there exists a unique solution for the stable paths problem. We define the simple path vector protocol (SPVP), a distributed algorithm for solving the stable paths problem. SPVP is intended to capture the dynamic behavior of BGP at an abstract level. If SPVP converges, then the resulting state corresponds to a stable paths solution. If there is no solution, then SPVP always diverges. In fact, SPVP can even diverge when a solution exists. We show that SPVP will converge to the unique solution of an instance of the stable paths problem if no dispute wheel exists     

DT-MRI fiber tracking: a shortest paths approach

We derive a new fiber tracking algorithm for DT-MRI that parts with the locally “greedy” paradigm intrinsic to conventional tracking algorithms. We demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer-generated DT-MRI data, for which well-known conventional tracking algorithms are shown to fail. Our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph. Voxels serve as vertices, and edges are included between neighboring voxels. We assign probabilities (weights) to edges using a Bayesian framework. Higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity. We compute optimal paths of maximum probability using computationally scalable shortest path algorithms. The salient features of our approach are: global optimality—unlike conventional tracking algorithms, local errors do not accumulate and one “wrong-turn” does not spell disaster; a target point is specified a priori; precise reconstruction is demonstrated for extremely low signal-to-noise ratio; impartiality to which of two endpoints is used as a seed; and, faster computation times than conventional all-paths tracking. We can use our new tracking algorithm in either a single-path tracking mode (deterministic tracking) or an all-paths tracking mode (probabilistic tracking).      

Class of communication networks with optimal connectivity

A network has optimal connectivity if the number of alternative paths between any pair of vertices is the greatest possible with the given number of lines and vertices. A new class of optimal configurations is described, which is sufficiently extensive to enable networks to be devised with almost any required connectivity, provided that the number of vertices is factorisable. Some implications for communication networks are discussed.     

双环网D (N,h)的最短路径选择算法

双环网是分布式系统常用的一种拓扑结构。它的寻径问题是人们关心的主要问题之一。本文给出了一个求双环网中任意两个节点间的最短路径算法,此算法所需时间为O(△),其中△是该网络的直径。     

Bandwidth-delay constrained path selection under inaccurate state information

A key issue in any QoS routing framework is how to compute a path that satisfies given QoS constraints. We focus on the path computation problem subject to bandwidth and delay constraints. This problem can be solved easily if the exact state information is available to the node computing the path. In practice, nodes have only imprecise knowledge of the network state. Reliance on outdated information and treating it as exact can significantly degrade the effectiveness of the path selection. We adopt a probabilistic approach in which the state parameters (available bandwidth and delay) are characterized by random variables. The goal is then to find the most-probable bandwidth-delay-constrained path (MP-BDCP). We provide efficient solutions for the MP-BDCP problem by decomposing it into the most-probable delay-constrained path (MP-DCP) problem and the most-probable bandwidth-constrained path (MP-BCP) problem. MP-DCP by itself is known to be NP-hard, necessitating the use of approximate solutions. We use the central limit theorem and Lagrange relaxation techniques to provide two complementary solutions for MP-DCP. These solutions are highly efficient, requiring on average a few iterations of Dijkstra's shortest path algorithm. As for MP-BCP, it can be easily transformed into a variant of the shortest path problem. Our MP-DCP and MP-BCP solutions are then combined to obtain a set of near-nondominated paths for the MP-BDCP problem. Decision makers can then select one or more of these paths based on a specific utility function. Extensive simulations demonstrate the efficiency of the proposed algorithmic solutions and, more generally, to contrast the probabilistic path selection approach with the standard threshold-based triggered approach.     

时延PCNN及其用于求解最短路径

本文在脉冲耦合神经网络(PCNN-Pulse Coupled Neural Network)的基础上,提出了时延脉冲耦合神经网络(DPCNN-Delay PCNN),并将其成功地用于求解最短路径,同时给出了基于DPCNN的最短路径求解算法.Caulfield与Kinser提出了用PCNN求解迷宫问题的方法,虽然他们的方法也可用于求解最短路径,但所需神经元的数量巨大,而本文的方法所需的神经元的数量远小于他们的方法.同时,本文的方法充分利用了DPCNN脉冲快速并行传播的特点,可迅速地求出最短路径,其所需的计算量仅正比于最短路径的长度,与路径图的复杂程度及路径图中的通路总数无关.计算机仿真结果表明,采用本文的方法,用少量的神经元就可迅速地求出最短路径.     

Performance enhancement for impairment-aware SRLG failure protection in wavelength-routed optical networks

With the increase of size and number of shared risk link groups (SRLGs) in WDM networks, path protection tends to have longer working paths and backup paths due to SRLG-disjoint constraints, which makes physical impairment a major concern in working path and backup path provisioning, particularly in large-sized all optical networks. As a simple and efficient algorithm, the working path first algorithm is often used for path protection against SRLG failures, where the working path is calculated first by using the shortest-path algorithm on the graph, followed by using the SRLG-disjoint shortest path as backup path. Compared with the working path, the backup path calculated after the working path in the working path first algorithm is more vulnerable to physical impairment, since it may be much longer than the working path. As a result, if we reject those connections that cannot meet the physical impairment requirement, with SRLGs the blocking probability of path protection will be much higher. We argue that impairment must be taken into account together with capacity efficiency in a comprehensive way during SRLG-disjoint working path and backup path selection. To solve this problem, we motivate the needs to study physical impairment-aware shared-path protection by considering two policies. Policy I uses two SRLG-disjoint least impairment paths as working path and backup path, respectively, and Policy II tries to benefit from both the shortest path and the least impairment path by choosing them intelligently. Analytical and simulation results show: (1) compared with impairment-unawareness, impairment-aware SRLG failure protection performs much better in terms of blocking probability especially with strong physical impairment constraints; (2) impairment-aware SRLG failure protection can significantly reduce physical-layer blocking probability; and (3) the algorithm based on Policy II achieves a good balance between capacity efficiency and physical impairment requirement.     

Distributed algorithms for computing shortest pairs of disjointpaths

Distributed algorithms for finding two disjoint paths of minimum total length from each node to a destination are presented. The algorithms have both node-disjoint and link-disjoint versions and provide each node with information sufficient to forward data on the disjoint paths. It is shown that this problem can be reduced to the problem of finding a minimal shortest path from each node to the destination in a modified network, and a distributed algorithm on the original network that simulates a shortest-paths algorithm running on the modified network is presented. The algorithm has a smaller space complexity than any previous distributed algorithm for the same problem, and a method for forwarding packets is presented that does not require any additional space complexity. A synchronous implementation of the algorithm is also presented and studied     

网树求解有向无环图中具有长度约束的最大不相交路径

对有向无环图中具有长度约束的最大不相交路径问题进行研究,该问题是求解图中两点间路径长度为k的最大不相交路径。为了对该问题进行求解,提出了贪婪搜索算法(GP, greedy path),该算法先将一个有向无环图转化为一棵深度为k+1的网树,然后计算每个网树节点的树根叶子路径数,并以此计算图中每个顶点的总路径数,之后从网树的第k+1层节点出发,在当前节点的双亲节点中选择未被使用且总路径数最小的双亲,以此形成一条优化的不相交路径,最后迭代这一过程,直到不再有新的不相交路径为止。GP算法的时间和空间复杂度分别为O(wkn(p+q))和O(kn(p+q)+n2)。为了测试GP算法的近似性,又建立了一种能够生成人工数据的算法,该算法能够准确地控制有向无环图中最大不相交路径的数量。通过该算法生成了大量测试用数据,实验结果表明GP算法较其他对比性算法具有良好的近似性且实际求解时间较短,验证了该方法的有效性和可行性。     

节点约束型最短路径的几何代数算法

面向网络分析应用中复杂条件约束下的最短路径求解问题,引入几何代数进行网络分析算法构造.建立了基于几何代数的网络模型和双边搜索算法,以寻找经过指定必经节点且弧段最少的最短路径求解为例,进行了算法实现.基于道路网络数据的分析显示,本算法利用外积运算直接判断约束节点,算法具有更好的通用性和较少的路径遍历次数,且在多对多路径求解及多用户并行求解上具有优势.     

Multi‐constrained Shortest Disjoint Paths for Reliable QoS Routing

Finding link‐disjoint or node‐disjoint paths under multiple constraints is an effective way to improve network QoS ability, reliability, and so on. However, existing algorithms for such scheme cannot ensure a feasible solution for arbitrary networks. We propose design principles of an algorithm to fill this gap, which we arrive at by analyzing the properties of optimal solutions for the multi‐constrained link‐disjoint path pair problem. Based on this, we propose the link‐disjoint optimal multi‐constrained paths algorithm (LIDOMPA), to find the shortest link‐disjoint path pair for any network. Three concepts, namely, the candidate optimal solution, the contractive constraint vector, and structure‐aware non‐dominance, are introduced to reduce its search space without loss of exactness. Extensive simulations show that LIDOMPA outperforms existing schemes and achieves acceptable complexity. Moreover, LIDOMPA is extended to the node‐disjoint optimal multi‐constrained paths algorithm (NODOMPA) for the multi‐constrained node‐disjoint path pair problem.     

The core-assisted mesh protocol

The core-assisted mesh protocol (CAMP) is introduced for multicast routing in ad hoc networks. CAMP generalizes the notion of core-based trees introduced for internet multicasting into multicast meshes that have much richer connectivity than trees. A shared multicast mesh is defined for each multicast group; the main goal of using such meshes is to maintain the connectivity of multicast groups even while network routers move frequently, CAMP consists of the maintenance of multicast meshes and loop-free packet forwarding over such meshes. Within the multicast mesh of a group, packets from any source in the group are forwarded along the reverse shortest path to the source, just as in traditional multicast protocols based on source-based trees. CAMP guarantees that within a finite time, every receiver of a multicast group has a reverse shortest path to each source of the multicast group. Multicast packets for a group are forwarded along the shortest paths front sources to receivers defined within the group's mesh. CAMP uses cores only to limit the traffic needed for a router to join a multicast group; the failure of cores does not stop packet forwarding or the process of maintaining the multicast meshes     

指挥决策实体层次结构设计方法

在指挥决策实体任务协作关系构成的协作交流网基础上,提出了一种设计指挥决策实体层次结构(指挥控制树)的新方法。该方法定义根节点到其他节点路径长度的最大值为树高,以构造树高最小的生成树为目标,对于取定的根节点,计算根节点到其他每个节点的唯一最短路径,对这些最短路径进行并操作得到的即为指挥控制树。最后结合一个案例,验证了应用该方法生成指挥控制树的可行性。     

An efficient pursuit automata approach for estimating stable all‐pairs shortest paths in stochastic network environments

This paper presents a new solution to the dynamic all‐pairs shortest‐path routing problem using a fast‐converging pursuit automata learning approach. The particular instance of the problem that we have investigated concerns finding the all‐pairs shortest paths in a stochastic graph, where there are continuous probabilistically based updates in edge‐weights. We present the details of the algorithm with an illustrative example. The algorithm can be used to find the all‐pairs shortest paths for the ‘statistical’ average graph, and the solution converges irrespective of whether there are new changes in edge‐weights or not. On the other hand, the existing popular algorithms will fail to exhibit such a behavior and would recalculate the affected all‐pairs shortest paths after each edge‐weight update. There are two important contributions of the proposed algorithm. The first contribution is that not all the edges in a stochastic graph are probed and, even if they are, they are not all probed equally often. Indeed, the algorithm attempts to almost always probe only those edges that will be included in the final list involving all pairs of nodes in the graph, while probing the other edges minimally. This increases the performance of the proposed algorithm. The second contribution is designing a data structure, the elements of which represent the probability that a particular edge in the graph lies in the shortest path between a pair of nodes in the graph. All the algorithms were tested in environments where edge‐weights change stochastically, and where the graph topologies undergo multiple simultaneous edge‐weight updates. Its superiority in terms of the average number of processed nodes, scanned edges and the time per update operation, when compared with the existing algorithms, was experimentally established. Copyright © 2008 John Wiley & Sons, Ltd.     

Priority‐based adaptive routing in NGEO satellite networks

In a non‐geostationary satellite constellation with inter satellite links (ISLs), there could be many shortest paths between two satellites in terms of hop count. An efficient routing algorithm should effectively use these paths in order to distribute traffic to ISLs in a balanced way and to improve the performance of the system. This paper presents and evaluates a novel priority‐based adaptive shortest path routing (PAR) scheme in order to achieve this goal. PAR sets the path towards the destination in a distributed manner, using a priority mechanism depending on the past utilization and buffering information of the ISLs. Moreover, to avoid unnecessary splitting of a flow and to achieve better utilization of ISLs, enhanced PAR (ePAR) scheme is proposed. This paper evaluates performance of the proposed techniques by employing an extensive set of simulations. Furthermore, since there are a number of ePAR parameters that should be adjusted depending on the network and traffic characteristics, a detailed analysis of ePAR scheme is provided to form a framework for setting the parameters. This paper also includes a method for adaptation of the proposed algorithms to minimum‐delay path routing. Copyright © 2006 John Wiley & Sons, Ltd.     

基于稳定分支的变权网络最优路径算法

有向网络的最短路问题在交通、通讯系统的最优传输路径中有重要应用.在通常的模型中,每条弧的权是给定的.但在实际问题中,弧的权会发生变化,例如在交通拥堵时运行时间会变长.如果当权发生变化时,要重新调用最短路算法,则浪费计算时间.本文提出最短路稳定性的概念,给出了关于最短路长度稳定、最优解稳定与稳定分支的命题与理论证明,在此基础上给出一种新的变权网络最短路径算法,利用权发生变化前的信息,减少计算量,提高计算效率.通过模拟实验验证了该算法的有效性.