Dynamic shortest path problems: Hybrid routing policies considering network disruptions

Traffic network disruptions lead to significant increases in transportation costs. We consider networks in which a number of links are vulnerable to these disruptions leading to a significantly higher travel time on these links. For these vulnerable links, we consider known link disruption probabilities and knowledge of transition probabilities for recovering from or getting into a disruption. We develop a framework based on dynamic programming in which we formulate and evaluate different known online and offline routing policies. Next to this, we develop computation-time-efficient hybrid routing policies. To test the efficiency of the different routing policies, we develop a test bed of networks based on a number of characteristics and analyze the results in terms of routes, cost performance and calculation times. Our results show that a significant part of the cost reduction can be obtained by considering only a limited part of the network in detail. The performance of our proposed hybrid policy is only slightly worse than the optimal policy.     

A Routing Algorithm with Candidate Shortest Path

An improved algorithm based on the next node routing principle is proposed in this paper.In this algorithm there is a column added to the classical routing table, in which the candidateshortest distance to the destination node is the entry. When a link fails, the new shortest path inthe nodes connected directly with the failure link can be found immediately (it is just thecandidate shortest path before failure). For all other nodes in which routing tables should bechanged, the required number of control messages and time for convergence are also less thanTajibnapis' algorithm and Predecessor algorithm. The message looping problem does not existin duplex loop networks and is radically improved in mesh networks. These statements areproved by the analysis and simulation in this paper. From the simulation results of a 30-nodemesh network, when one link goes down, the total number of control messages generatedduring convergence with this algorithm on the average is about 30% of Tajibnapis' algorithm.The iterations required is 50% of Tajibnapis' algorithm. The memory space required andcomputation complexity in nodes are almost the same as the two algorithms mentioned aboveand the algorithm implementation is as easy as well.     

Energy-aware IP traffic engineering with shortest path routing

Internet energy consumption is rapidly becoming a critical issue due to the exponential traffic growth and the rapid expansion of communication infrastructures worldwide. We address the problem of energy-aware intra-domain traffic engineering in networks operated with a shortest path routing protocol. We consider the problem of switching off (putting in sleep mode) network elements (links and routers) and of adjusting the link weights so as to minimize the energy consumption as well as a network congestion measure. To tackle this multi-objective optimization problem with priority (first minimize the energy consumption and then the network congestion), we propose a Mixed Integer Linear Programming based algorithm for Energy-aware Weights Optimization (MILP-EWO). Our heuristic exploits the Interior Gateway Protocol Weight Optimization (IGP-WO) algorithm for optimizing the OSPF link weights so as to minimize the total cost of link utilization. The computational results obtained for eight real network topologies and different types of traffic matrices show that it is possible to switch off a substantial number of nodes and links during low and moderate traffic periods, while guaranteeing that network congestion is low enough to ensure service quality. The proposed approach is also validated on two networks of emulated Linux routers.     

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     

基于最短路径搜索序列编码的多下一跳路由

多下一跳路由较之单下一跳路由有许多天然的优势,通过分析现有多下一跳路由实现机制下的路由算法,提出了基于最短路径搜索序列编码的多下一跳路由.针对SPT(shortest path tree)路由实现机制无法利用等距离邻居节点之间链路的问题,提出了采用Dijkstra算法对网络节点编码赋值的思想.该方法可以对节点进行严格有序的赋值,规范了链路传输方向,有效地避免了环路,提高了网络资源利用率.仿真分析结果表明了该算法的可行性和有效性.     

Reduction approaches for robust shortest path problems

We investigate the uncertain versions of two classical combinatorial optimization problems, namely the Single-Pair Shortest Path Problem (SP-SPP) and the Single-Source Shortest Path Problem (SS-SPP). The former consists of finding a path of minimum length connecting two specific nodes in a finite directed graph G; the latter consists of finding the shortest paths from a fixed node to the remaining nodes of G. When considering the uncertain versions of both problems we assume that cycles may occur in G and that arc lengths are (possibly degenerating) nonnegative intervals. We provide sufficient conditions for a node and an arc to be always or never in an optimal solution of the Minimax regret Single-Pair Shortest Path Problem (MSP-SPP). Similarly, we provide sufficient conditions for an arc to be always or never in an optimal solution of the Minimax regret Single-Source Shortest Path Problem (MSS-SPP). We exploit such results to develop pegging tests useful to reduce the overall running time necessary to exactly solve both problems.     

时延受限组播路由的最短路径加速算法求解

分析了时延受限的Steiner树问题,总结了在构建组播树过程中的代价和计算复杂度变化规律,并根据实际网络环境,从优化最短路径出发,提出了一种基于优化最短路径的时延受限组播路由算法AOSPMPH。该算法以MPH算法为基础,利用Floyd最短路径优化算法求出节点对之间的最短路径,选择满足时延要求的最小代价路径加入组播树,进而产生一棵满足时延约束的最小代价组播树。仿真结果表明,AOSPMPH不但能正确地构造时延约束组播树,而且其代价和计算复杂度与其他同类算法相比得到了优化。     

Multi-objective and multi-constrained non-additive shortest path problems

Shortest path problems appear as subproblems in numerous optimization problems. In most papers concerning multiple objective shortest path problems, additivity of the objective is a de-facto assumption, but in many real-life situations objectives and criteria, can be non-additive. The purpose of this paper is to give a general framework for dominance tests for problems involving a number of non-additive criteria. These dominance tests can help to eliminate paths in a dynamic programming framework when using multiple objectives. Results on real-life multi-objective problems containing non-additive criteria are reported. We show that in many cases the framework can be used to efficiently reduce the number of generated paths.     

Privacy preserving shortest path routing with an application to navigation

Mobile navigation is a frequently used application, especially with the increasing proliferation of online geographical data. However, the origin and destination are often private information closely tied to a user’s personal life. Sharing those with an online map provider greatly increases the chance of the user being profiled. Contrary to existing location privacy problems, the origin and the destination are essential for finding the shortest path in a realtime traffic setting. In this paper, we show that the problem can be solved with Private Information Retrieval (PIR) techniques without disclosing the origin or the destination. We analyze the cost associated with this approach and propose a practical solution with the assumption of a semi-honest third party to improve the efficiency. The proposed practical solution only introduces encryption overhead over the plain scenario where the path is returned by knowing the origin and destination.     

Neural networks for shortest path computation and routing incomputer networks

The application of neural networks to the optimum routing problem in packet-switched computer networks, where the goal is to minimize the network-wide average time delay, is addressed. Under appropriate assumptions, the optimum routing algorithm relies heavily on shortest path computations that have to be carried out in real time. For this purpose an efficient neural network shortest path algorithm that is an improved version of previously suggested Hopfield models is proposed. The general principles involved in the design of the proposed neural network are discussed in detail. Its computational power is demonstrated through computer simulations. One of the main features of the proposed model is that it will enable the routing algorithm to be implemented in real time and also to be adaptive to changes in link costs and network topology.     

消息路径:UML协作图的复杂性度量

针时面向对象软件的复杂性,提出了一种面向UML协作图的软件动态复杂性度量方法--消息路径.基于UML协作图中角色对象间的消息流以及所定义的不同类别的信息标记,给出消息路径图的构造方法和基于消息路径图的面向对象软件动态复杂性度量模型.在该模型中,建立了一组复杂性度量指标,并对这些指标的意义进行了阐述.结合具体实例,给出了消息路径图和各项指标值,并且比较了不同实例的度量结果,表明了所提出度量方法的可行性和实用性.     

Parallel algorithms for shortest path problems in polygons

Given ann-vertex simple polygon we address the following problems: (i) find the shortest path between two pointss andd insideP, and (ii) compute the shortestpath tree between a single points and each vertex ofP (which implicitly represents all the shortest paths). We show how to solve the first problem inO(logn) time usingO(n) processors, and the more general second problem inO(log² n) time usingO(n) processors, and the more general second problem inO(log² n) time usingO(n) processors for any simple polygonP. We assume the CREW RAM shared memory model of computation in which concurrent reads are allowed, but no two processors should attempt to simultaneously write in the same memory location. The algorithms are based on the divide-and-conquer paradigm and are quite different from the known sequential algorithmsResearch supported by the Faculty of Graduate Studies and Research (McGill University) grant 276-07     

Solving fuzzy shortest path problems by neural networks

In this paper, we introduce the neural networks for solving fuzzy shortest path problems. The penalization of the neural networks is realized after transforming into crisp shortest path model. The procedure and efficiency of this approach are shown with numerical simulations.     

A numerical method for solving shortest path problems

Chebyshev pseudo-spectral method is one of the most efficient methods for solving continuous-time optimization problems. In this paper, we utilize this method to solve the general form of shortest path problem. Here, the main problem is converted into a nonlinear programming problem and by solving of which, we obtain an approximate shortest path. The feasibility of the nonlinear programming problem and the convergence of the method are given. Finally, some numerical examples are considered to show the efficiency of the presented method over the other methods.     

On supporting high-throughput routing metrics in on-demand routing protocols for multi-hop wireless networks

Researchers have proposed routing metrics other than hop count, such as ETX (expected transmission count) and ETT (expected transmission time), to find routes with high throughput. These metrics are inherently suitable to be used in source routing protocols such as DSR, because link state information needs to be collected for the calculation of the shortest path. In this paper, we propose an efficient and generalized approach called accumulated path metric (APM) for supporting high-throughput metrics (HTMs) in on-demand routing protocols. One advantage of APM is that it is able to find the shortest path, in terms of a particular metric, without collecting topology information and without running a shortest-path algorithm. This will significantly simplify the existing design of supporting HTMs in DSR. We present a proof of the correctness of APM. Moreover, we address the problem of duplicate RREQ (route request) transmissions with existing HTM schemes and present a broadcast ordering (BO) technique to suppress unnecessary RREQ transmissions. We study the performance of APM and BO in both AODV and DSR, and the results verify the effectiveness of the proposed approaches.     

Algorithms for a special class of state-dependent shortest path problems with an application to the train routing problem

We study the state-dependent shortest path problem and focus on its application to the Single Train Routing Problem consisting of a rail network with only double-track segments, where the objective is to route one train through an empty network as fast as possible. We show that the Single Train Routing Problem is NP-hard. We investigate the solution properties and present sufficient conditions for optimality. Different conditions on the parameters are given to guarantee that certain local route selection is optimal. Then, a dynamic programming heuristic is introduced and conditions when the proposed heuristic can obtain the optimal solution in polynomial time are also discussed. Experimental results show the efficiency of the proposed heuristics for general problem settings.     

A biologically inspired solution for fuzzy shortest path problems

By considering the uncertainty that exists in the edge weights of the network, fuzzy shortest path problems, as one of the derivative problems of shortest path problems, emerge from various practical applications in different areas. A path finding model, inspired by an amoeboid organism, Physarum polycephalum, has been shown as an effective approach for deterministic shortest path problems. In this paper, a biologically inspired algorithm called Fuzzy Physarum Algorithm (FPA) is proposed for fuzzy shortest path problems. FPA is developed based on the path finding model, while utilizing fuzzy arithmetic and fuzzy distance to deal with fuzzy issues. As a result, FPA can represent and handle the fuzzy shortest path problem flexibly and effectively. Distinct from many existing methods, no order relation has been assumed in the proposed FPA. Several examples, including a tourist problem, are given to illustrate the effectiveness and flexibility of the proposed method and the results are compared with existing methods.     

On open shortest path first related network optimisation problems

The paper deals with flow allocation problems in IP networks using open shortest path first (OSPF) routing. Its main purpose is to discuss and propose methods for finding settlements of OSPF link weight system realising the assumed demand pattern for the given network resources (links capacities). Such settlements can result in a significantly better network performance, as compared with the simplified weight setting heuristics typically used nowadays. Although the configuration of the link weight system is primarily done in the network planning phase, still additional re-optimisations are feasible, and in fact essential, in order to cope with major changes in traffic conditions and with major resources’ failures and rearrangements.

The paper formulates a relevant OSPF routing optimisation problem, proves its NP-completeness, and discusses possible heuristic approaches and related optimisation methods for solving it. Two basic approaches are considered (the direct approach and the two-phase approach) and the resulting optimisation algorithms are presented. The considerations are illustrated with numerical results.     

A cost matrix agent for shortest path routing in ad hoc networks

Wireless ad hoc networks do not rely on an existing infrastructure. They are organized as a network with nodes that act as hosts and routers to treat packets. With their frequent changes in topology, ad hoc networks do not rely on the same routing methods as for pre-established wired networks; they require routing methods for mobile wireless networks. To select a path from a source to a destination in dynamic ad hoc networks, an efficient and reliable routing method is very important. In this paper, we introduce a cost-matrix-based routing algorithm. An agent node creates topology information in the form of the adjacency-cost matrix which shows link costs of the network.Based on the adjacency-cost matrix, the minimum-cost matrix and the next-node matrices can be calculated. Based on the minimum-cost matrix and the next-node matrices, the minimum cost between source and destination nodes and between intermediate nodes on the minimum-cost paths can be calculated.The matrices are periodically distributed by the agent to the other nodes. Based on the minimum-cost matrix and the next-node matrices, each node decides the minimum-cost path to its destination. Because none of the nodes except the agent needs to gather network topology information, the control overhead of the proposed method is small compared with those of the general table-driven routing protocols.     

Ant-based routing for wireless multimedia sensor networks using multiple QoS metrics

In wireless sensor networks, most routing protocols consider energy savings as the main objective and assume data traffic with unconstrained delivery requirements to be a given. However, the introduction of video and imaging sensors unveils additional challenges. The transmission of video and imaging data requires both energy efficiency and QoS assurance (end-to-end delay and packet loss requirements), in order to ensure the efficient use of sensor resources as well as the integrity of the information collected. This paper presents a QoS routing model for Wireless Multimedia Sensor Networks (WMSN). Moreover, based on the traditional ant-based algorithm, an ant-based multi-QoS routing metric (AntSensNet) is proposed. The AntSensNet protocol builds a hierarchical structure on the network before choosing suitable paths to meet various QoS requirements from different kinds of traffic, thus maximizing network utilization, while improving its performance. In addition, AntSensNet is able to use a efficient multi-path video packet scheduling in order to get minimum video distortion transmission. Finally, extensive simulations are conducted to assess the effectiveness of this novel solution and a detailed discussion regarding the effects of different system parameters is provided. Compared to typical routing algorithms in sensor networks and the traditional ant-based algorithm, this new algorithm has better convergence and provides significantly better QoS for multiple types of services in wireless multimedia sensor networks.