Transient chaotic neural network-based disjoint multipath routing for mobile ad-hoc networks

Due to mobility of wireless hosts, routing in mobile ad-hoc networks (MANETs) is a challenging task. Multipath routing is employed to provide reliable communication, load balancing, and improving quality of service of MANETs. Multiple paths are selected to be node-disjoint or link-disjoint to improve transmission reliability. However, selecting an optimal disjoint multipath set is an NP-complete problem. Neural networks are powerful tools for a wide variety of combinatorial optimization problems. In this study, a transient chaotic neural network (TCNN) is presented as multipath routing algorithm in MANETs. Each node in the network can be equipped with a neural network, and all the network nodes can be trained and used to obtain optimal or sub-optimal high reliable disjoint paths. This algorithm can find both node-disjoint and link-disjoint paths with no extra overhead. The simulation results show that the proposed method can find the high reliable disjoint path set in MANETs. In this paper, the performance of the proposed algorithm is compared to the shortest path algorithm, disjoint path set selection protocol algorithm, and Hopfield neural network (HNN)-based model. Experimental results show that the disjoint path set reliability of the proposed algorithm is up to 4.5 times more than the shortest path reliability. Also, the proposed algorithm has better performance in both reliability and the number of paths and shows up to 56% improvement in path set reliability and up to 20% improvement in the number of paths in the path set. The proposed TCNN-based algorithm also selects more reliable paths as compared to HNN-based algorithm in less number of iterations.     

An optimal inherently stabilizing routing algorithm for star P2P overlay networks

Star graphs possess many desirable properties such as scalable node degrees and diameters, which are essential to facilitate reduced routing table sizes and low maximum path length for routing in large P2P networks. In addition, because a large number of disjoint paths are available and each data/replica in an n‐star can be placed in an (n − 1)‐star, load balancing and alleviation of network bottlenecks can be implemented in star P2P overlay networks. Therefore, star networks have been proposed as viable alternatives to existing overlay topologies for large P2P networks. In this paper, we propose an optimal stabilizing and inherently stabilizing algorithm for routing messages over all disjoint paths between two peers in a star P2P overlay network. The algorithm is optimal in terms of its time complexity in rounds and the length of the longest path traversed by the messages, and fault tolerant due to being stabilizing and inherently stabilizing, allowing the system to withstand transient faults. The algorithm can be used to increase network reliability and survivability in P2P networks. In addition, the usage of all disjoint paths to route messages between two peers leads to increased network bandwidth while distributing the communication overhead across the network and eliminating network bottlenecks in P2P networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Linear time distributed construction of colored trees for disjoint multipath routing

Disjoint multipath routing (DMPR) is an effective strategy to achieve robustness in networks where data is forwarded along multiple link- or node-disjoint paths. DMPR poses significant challenges in terms of obtaining loop-free multiple (disjoint) paths and effectively forwarding data over the multiple paths, the latter being particularly significant in datagram networks. One approach to reduce the number of routing table entries for disjoint multipath forwarding is to construct two trees, namely red and blue, rooted at a destination node such that the paths from a source to the destination on the two trees are link/node-disjoint. This paper develops the first distributed algorithm for constructing the colored trees whose running time is linear in the number of links in the network. The paper also demonstrates the effectiveness of employing generalized low-point concept rather than traditional low-point concept in the DFS-tree to reduce the average path lengths on the colored trees.     

一种交叉立方体网络的并行路由算法

Efe提出的交叉立方体是超立方体的一种变型，其某些性质优于超立方体。在高性能的并行计算机系统中，信息通过若干条内结点互不交叉的路径并行传输，这些路径的长度将直接影响并行计算的性能。该文提出了一种时间复杂度为o(n2)的交叉立方体网络并行路由算法，可输出源点u到目的点v的3条并行路径P0,P1,P2，并且满足：(1)|P0|= u到v的距离；(2)|Pi|≤u到v的距离+3(i=1,2)。这说明该算法是通信高效的。     

All-to-all disjoint multipath routing using cycle embedding

In this paper, we evaluate the performance of disjoint multipath routing approaches for all-to-all routing in packet-switched networks with respect to packet overhead, path length, and routing table size. We develop a novel approach based on cycle embedding to obtain two node-disjoint paths between all source–destination pairs with reduced number of routing table entries maintained at a node (hence the reduced lookup time), small average path length, and less packet overhead. We study the trade-off between the number of routing table entries maintained at a node and the average length of the two disjoint paths by: (a) formulating the cycle-embedding problem as an integer linear program; and (b) developing a heuristic. We show that the number of routing table entries at a node may be reduced to at most two per destination using cycle-embedding approach if the average length of the disjoint paths are allowed to exceed the minimum by 25%.     

Disjoint multipath routing using colored trees

Multipath routing (MPR) is an effective strategy to achieve robustness, load balancing, congestion reduction, and increased throughput in computer networks. Disjoint multipath routing (DMPR) requires the multiple paths to be link- or node-disjoint. Both MPR and DMPR pose significant challenges in terms of obtaining loop-free multiple (disjoint) paths and effectively forwarding the data over the multiple paths, the latter being particularly significant in IP datagram networks.This paper develops a two-disjoint multipath routing strategy using colored trees. Two trees, red and blue, that are rooted at a designated node, called the drain, are formed. The paths from a given source to the drain on the two trees are link- or node-disjoint. The colored tree approach requires every node to maintain only two preferred neighbors for each destination, one on each tree. This paper (1) formulates the problem of colored-trees construction as an integer linear program (ILP); and (2) develops the first distributed algorithm to construct the colored trees using only local information. We demonstrate the effectiveness of the distributed algorithm by evaluating it on grid and random topologies and comparing to the optimal obtained by solving the ILP.     

Nearly optimal one-to-many parallel routing in star networks

Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and the running time of our algorithm is bounded by O(n²). More specifically, given a node s and n-1 other nodes {t₁, t₂ , …, t_n-1} in the n-star network, our algorithm constructs n-1 node-disjoint paths P₁, P₂, …, P_n-1, where P_i is a path from s to t_j of length at most dist(s, t_j)+6 and dist(s, t _j) is the distance, i.e., the length of a shortest path, from s to t_j, for i=1, 2, …, n-1.The best bound on the path length by previously known algorithms for the same problem is 5(n-2)≈10Δ_n/3, where Δ_n=max{dist(s, t)} is the diameter of the n-star network     

无线传感器网络一种不相交路径路由算法

无线传感器网络经常被用来采集物理数据,监测环境变化.由于低功耗无线通信不确定性、链路质量不稳定性以及节点失效等问题,传感器网络很容易导致路由数据包丢失.为了提高网络路由的可靠性,人们提出多路径路由算法.多路径路由中源节点到目的节点的多条路径可能含有公共节点,或者公共边,如果公共节点或者公共链路失效,则这个数据包也丢失,因此又有人提出不相交多路径路由算法.不相交多路径路由算法又分为链路不相交多路径路由算法和节点不相交多路径路由算法.提出了一种不相交路径路由算法,可以将感知节点采集到的数据通过不相交路径传送到汇聚节点,提高路由的可靠性.而且,这个算法还可以很方便地应用到多Sink节点的网络当中.该路由算法用到的路由表大小为|K|,其中|K|表示路径数.算法的运行时间复杂度是O(|L|),其中|L|表示网络中的边数.     

Near-optimal broadcast in all-port wormhole-routed hypercubes usingerror-correcting codes

A new broadcasting method is presented for hypercubes with wormhole routing mechanism. The communication model assumed allows an n-dimensional hypercube to have at most n concurrent 110 communications along its ports. It further assumes a distance insensitivity of (n+1) with no intermediate reception capability for the nodes along the communication path. The approach is based on determination of the set of nodes (called stations) in the hypercube such that for any node in the network there is a station at distance of at most 1. Once stations are identified, parallel disjoint paths are formed from the source to all stations. The broadcasting is accomplished first by sending the message to all stations which will in turn inform the rest of the nodes of the message. To establish node-disjoint paths between the source node and all stations, we introduce a new routing strategy. We prove that multicasting can be done in one routing step as long as the number of destination nodes are at most n in an n-dimensional hypercube. The number of broadcasting steps using our routing is equal to or smaller than that obtained in an earlier work; this number is optimal for all hypercube dimensions n⩽12, except for n=10     

Routing permutations on baseline networks with node-disjoint paths

Permutation is a frequently-used communication pattern in parallel and distributed computing systems and telecommunication networks. Node-disjoint routing has important applications in guided wave optical interconnects where the optical "crosstalk" between messages passing the same switch should be avoided. In this paper, we consider routing arbitrary permutations on an optical baseline network (or reverse baseline network) with node-disjoint paths. We first prove the equivalence between the set of admissible permutations (or semipermutations) of a baseline network and that of its reverse network based on a step-by-step permutation routing. We then show that an arbitrary permutation can be realized in a baseline network (or a reverse baseline network) with node-disjoint paths in four passes, which beats the existing results [M. Vaez et al., (2000)], [G. Maier et al., (2001)] that a permutation can be realized in an n /spl times/ n banyan network with node-disjoint paths in O(n/sup 1/2/) passes. This represents the currently best-known result for the number of passes required for routing an arbitrary permutation with node-disjoint paths in unique-path multistage networks. Unlike other unique path MINs (such as omega networks or banyan networks), only baseline networks have been found to possess such four-pass routing property. We present routing algorithms in both self-routing style and central-controlled style. Different from the recent work in [Y. Yang et al., (2003)], which also gave a four-pass node-disjoint routing algorithm for permutations, the new algorithm is efficient in transmission time for messages of any length, while the algorithm in [Y. Yang et al., (2003)] can work efficiently only for long messages. Comparisons with previous results demonstrate that routing in a baseline network proposed in this paper could be a better choice for routing permutations due to its lowest hardware cost and near-optimal transmission time.     

移动WSN节点不相交多路径路由算法

针对移动无线传感器网络不相交多路径路由中的路径断裂问题,提出基于HSV色彩空间的节点不相交多路径路由算法。采用HSV色彩空间模型为每条链路建立数值化的（h,s,v）三元组,使其属于不同的色彩平面,以寻找从源节点到目标节点的多条节点不相交路径。针对节点移动问题,设计基于可变时间间隔链路接收信号强度指示值探测的不相交多路径维护机制,该机制无需借助地理位置信息。实验结果表明,当使用3条路径传输时,该算法的数据传输成功率可达到80％以上,而对比的经典算法均低于70％。此外,其在网络吞吐量、能量消耗等方面也具有较好的性能。     

A parallel routing algorithm on recursive cube of rings networks employing Hamiltonian circuit Latin square

Recursive cube of rings (RCR) networks [Y. Sun, P. Cheung, X. Lin, Recursive cube of rings: a new topology for interconnection networks, IEEE Trans. Parallel Dist. Syst. 11 (3) (2000) 275-286] can be widely used in the design and implementation of parallel processing architectures. In this paper, we investigate the routing of a message on RCR networks, that is a key to the performance of this network. We would like to transmit k+1 packets from a source node to a destination node simultaneously along paths on RCR networks, the ith packet will traverse along the ith path (1?i?k+1). In order for all packets to arrive at a destination node quickly and securely, the ith path must be node-disjoint from all other paths. For construction of these paths, employing Hamiltonian circuit Latin square (HCLS), we present O(n²) parallel routing algorithm on RCR networks.     

Adaptive Fault-Tolerant Multicast in Hypercube Multicomputers

Fault-tolerant message routing mechanism is a key to the performance of reliable multicomputers. Multicast refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. This paper presents two types of partially adaptive fault tolerant multicast algorithms. The Type A algorithm can deliver messages to all destinations through shortest paths if each fault-free node has at most one faulty neighbor. The Type B algorithm can deliver messages to all destinations if the total number of faulty links and faulty nodes is less than the dimension of the hypercube. The proposed algorithms have the following important features: they are distributed, they only require local information to determine the paths, and they need very little additional message overhead. The performance of the algorithms, measured by the traffic created by the communication, is very close to that in fault-free hypercubes.     

点对点并行路由算法及容错性概率分析

用概率性分析方法,研究了在结点错误概率性分布的情形下,超立方体网络的点对点并行路由算法,并对算法的容错性概率、路径长度、算法复杂性进行了严格的推导。提出的算法是基于任意给定两个正确结点可以找出n条不相交的路径。分析了算法保证一条或多条路径同时联通的概率达到99.99%时结点的错误概率上界,同时考虑了两点间的海明距离变化,得出了较好的理论结论与计算结果。方法为研究超立方体网络容错性与并行路由算法提供了一种新的途径与新的考虑角度,具有更一般与更接近实际的意义。     

Construction of vertex-disjoint paths in alternating group networks

The existence of parallel node-disjoint paths between any pair of nodes is a desirable property of interconnection networks, because such paths allow tolerance to node and/or link failures along some of the paths, without causing disconnection. Additionally, node-disjoint paths support high-throughput communication via the concurrent transmission of parts of a message. We characterize maximum-sized families of parallel paths between any two nodes of alternating group networks. More specifically, we establish that in a given alternating group network AN _n , there exist n−1 parallel paths (the maximum possible, given the node degree of n−1) between any pair of nodes. Furthermore, we demonstrate that these parallel paths are optimal or near-optimal, in the sense of their lengths exceeding the internode distance by no more than four. We also show that the wide diameter of AN _n is at most one unit greater than the known lower bound D+1, where D is the network diameter.     

MANET节点不相关的多路路由算法

针对不相关路由路径之闯可能存在特定关键节点问题,提出一种特定节点不相关多路路由算法,通过寻找关键节点,使数据报文经单路径到达关键节点的上一跳节点后,向多条不相关路径的节点进行转发,使数据报文可以同时在多条节点不相关的路径上路由到达目的节点。仿真实验结果表明,如果存在关键节点,该算法能够提高分组投递率、降低端到端延迟;如果不存在关键节点,该算法的性能与节点不相关算法相当。     

Fully symmetric swapped networks based on bipartite cluster connectivity

The class of swapped or OTIS (optical transpose interconnect system) networks, built of n copies of an n-node cluster by connecting node i in cluster j to node j in cluster i for i≠j, has been studied extensively. One problem with such networks is that node i of cluster i has no intercluster link. This slight asymmetry complicates a number of algorithms and hinders both theoretical investigations and practical pursuits, such as building parallel node-disjoint paths for fault tolerance. We introduce biswapped networks that are fully symmetric and have cluster connectivity very similar to swapped/OTIS networks. We derive basic topological parameters, present a simple distributed shortest-path routing algorithm, and point to a number of other interesting properties under investigation for biswapped networks.     

基于NPV广义超立方体最佳容错路由算法

在网络可靠性研究中,设计较好的容错路由策略、尽可能多地记录系统中最优通路信息,一直是一项重要的研究工作.超立方体系统的容错路由算法分为可回溯算法和无回溯算法.一般说来,可回溯算法的优点是容错能力强:只要消息的源节点和目的节点有通路,该算法就能够找到把消息传递到目的地的路径;其缺点是在很多情况下传递路径不能按实际存在的最短路径传递.其代表是深度优先搜索(DFS)算法.无回溯算法是近几年人们比较关注的算法.该算法通过记录各邻接节点的故障信息,给路由算法以启发信息,使消息尽可能按实际存在的最短路径传递.这些算法的共同缺点是只能计算出Hamming距离不超过n的路由.在n维超立方体系统连通图中,如果系统存在大量的故障,不少节点对之间的最短路径大于n,因此,这些算法的容错能力差.提出了一个实例说明采用上述算法将遗失60%的路由信息.另外,由于超立方体的结构严格,实际中的真正超立方体系统不多.事实上,不少的网络系统可转换为具有大量错误节点和错误边的超立方体系统.因此,研究能适应具有大量错误节点和错误边的超立方体系统的容错路由算法是一个很有实际价值的工作.研究探讨了:(1) 定义广义超立方体系统;(2) 在超立方体系统中提出了节点通路向量(NPV)概念及其计算规则;(3) 提出了中转点技术,使得求NPV的计算复杂度降低到O(n);(4) 提出了基于NPV的广义超立方体系统最佳容错路由算法(OFTRS),该算法是一种分布式的和基于相邻节点信息的算法.由于NPV记录了超立方体系统全部最优通路和次最优通路的信息,在具有大量故障的情况下,它不会遗漏任何一条最优通路和次最优通路信息,从而实现了高效的容错路由.在这一点上,它优于其他算法.     

Leapfrog: Optimal Opportunistic Routing in Probabilistically Contacted Delay Tolerant Networks

Delay tolerant networks (DTNs) experience frequent and long lasting network disconnection due to various reasons such as mobility, power management, and scheduling. One primary concern in DTNs is to route messages to keep the end-to-end delivery delay as low as possible. In this paper, we study the single-copy message routing problem and propose an optimal opportunistic routing strategy – Leapfrog Routing – for probabilistically contacted DTNs where nodes encounter or contact in some fixed probabilities. We deduce the iterative computation formulate of minimum expected opportunistic delivery delay from each node to the destination, and discover that under the optimal opportunistic routing strategy, messages would be delivered from high-delay node to low-delay node in the leapfrog manner. Rigorous theoretical analysis shows that such a routing strategy is exactly the optimal among all possible ones. Moreover, we apply the idea of Reverse Dijkstra algorithm to design an algorithm. When a destination is given, this algorithm can determine for each node the routing selection function under the Leapfrog Routing strategy. The computation overhead of this algorithm is only O(n ²) where n is the number of nodes in the network. In addition, through extensive simulations based on real DTN traces, we demonstrate that our algorithm can significantly outperform the previous ones.     

Deterministic broadcasting in ad hoc radio networks

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time . Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop efficient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Received: January 2000 / Accepted: June 2001