Node-disjoint paths in incomplete WK-recursive networks

The incomplete WK-recursive networks have been recently proposed to relieve the restriction on the sizes of the WK-recursive networks. In this paper, a maximal set of node-disjoint paths is constructed between arbitrary two nodes of an incomplete WK-recursive network. The effectiveness of the constructed paths is verified by both theoretic analysis and extensive experiments. A tight upper bound on the maximal length is suggested. On the other hand, experimental results show that for arbitrary two nodes, the expected maximal length is not greater than twice their distance and about equal to the diameter. When the two nodes are the farthest pair, the maximal length is not greater than twice the diameter and the expected maximal length is not greater than 1.5 times the diameter.     

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     

Some topological and combinatorial properties of WK-recursive mesh and WK-pyramid interconnection networks

The WK-recursive mesh and WK-pyramid networks are recursively defined hierarchical interconnection networks with excellent properties which well idealize them as alternatives for mesh and traditional pyramid interconnection topologies. They have received much attention due to their favorable attributes such as small diameter, large connectivity, and high degree of scalability and expandability. In this paper, we deal with pancyclicity and surface area of these networks. These properties are of great importance in the implementation of a variety of parallel algorithms in multicomputers. We show that WK-recursive mesh network is 1-partially pancyclic, i.e. any cycle of length 3, 4, 6,…, and N can be constructed in the WK-recursive mesh. Also, we prove that the WK-pyramid is pancyclic, that is all cycles of length 3, 4, … , and N can be formed in a WK-pyramid. It is also proved that two link-disjoint Hamiltonian paths/cycles can be embedded in the WK-recursive mesh/WK-pyramid. We then study the surface area of WK-recursive mesh and WK-pyramid networks and put forth some equations for calculating the surface area in these networks.     

Study of General Incomplete Star Interconnection Networks

IIntroduct1OllThe star graph【1]proposed as a particular case ofC叫ley graphs[ZJ Is vertex－and edge－symmetric．strongly hlerarchlcal,maximally tault－tolerant,strongly resilient and has diameter and node degreethat are superior to those of a slmll。－slied hypercube(which Is also a Cnyley graph)IOr parallelcomputers[3]．MNor references can be found In studying the star graph regarding its propertiesllJ,e毗edding cwabllity[4],communication c叩劝ility[5－71,andfanfaut－toierm尬 cap劝ility…     

Study of General Icomplete Star Interconnection Networks

The star networks,which were originally proposed by Akers and Harel,have suffered from a rigorous restriction on the number of nodes.The general incomplete star networks(GISN) are proposed in this paper to relieve this restriction.An efficient labeling scheme for GISN is given,and routing and broadcasting algorithms are also presented for GIS.The communication diameter of GISN is shown to be bounded by 4n-7.The proposed single node broadcasting algorithm is optimal with respect to time complexity O(nlog2n).     

基于大功率消息广播的DTMSN路由机制

提出一种基于基站大功率信号广播的延迟容忍移动传感器网络消息路由机制(High-power Broadcasting based Routing scheme,HBR)。该机制使用两个通信频率f₁ 和f₂,基站以恒定大功率在频率f₁上广播已经接收到的消息,网络中传感器节点根据基站广播信息计算自身转发概率并清理冗余消息副本,节点间利用频率f₂进行通信。为进一步提升网络性能,HBR优先传输转发阈值(M)小且生存时间短的消息,并合理进行消息队列管理。仿真结果表明,与几种经典的路由机制相比,HBR在消息传输成功率、传输延迟方面有着一定的优势。     

Independent spanning trees vs. edge-disjoint spanning trees in locally twisted cubes

Fault-tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple spanning trees with a specific property in the underlying graph of a network to serve as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and of security. A set of spanning trees in a graph is said to be edge-disjoint if these trees are rooted at the same node without sharing any common edge. Hsieh and Tu [S.-Y. Hsieh, C.-J. Tu, Constructing edge-disjoint spanning trees in locally twisted cubes, Theoretical Computer Science 410 (2009) 926-932] recently presented an algorithm for constructing n edge-disjoint spanning trees in an n-dimensional locally twisted cube. In this paper, we prove that indeed all spanning trees constructed by their algorithm are independent, i.e., any two spanning trees are rooted at the same node, say r, and for any other node v≠r, the two different paths from v to r, one path in each tree, are internally node-disjoint.     

The Grid-Pyramid: A Generalized Pyramid Network

The Pyramid network is a desirable network topology used as both software data-structure and hardware architecture. In this paper, we propose a general definition for a class of pyramid networks that are based on grid connections between the nodes in each level. Contrary to the conventional pyramid network in which the nodes in each level form a mesh, the connections between these nodes may also be according to other grid-based topologies such as the torus, hypermesh or WK-recursive. Such pyramid networks form a wide class of interconnection networks that possess rich topological properties. We study a number of important properties of these topologies for general-purpose parallel processing applications. In particular, we prove that such pyramids are Hamiltonian-connected, i.e. for any arbitrary pair of nodes in the network there exists at least one Hamiltonian path between the two given nodes, and pancyclic, i.e. any cycle of length 3, 4 … and N, can be embedded in a given N-node pyramid network. It is also proven that two link-disjoint Hamiltonian cycles exist in the torus-pyramid and hypermesh-pyramid networks.     

Hamiltonian connectivity of the WK-recursive network with faulty nodes

A graph G is said to be Hamiltonian-connected if there is a Hamiltonian path between every two distinct nodes of G. Let F denote the set of faulty nodes of G. Then, G is |F|-node Hamiltonian-connected if G-F is Hamiltonian-connected. We use K(d,t) to denote a WK-recursive network of level t, each of whose basic modules is a d-node complete graph. Compared with other networks, it is rather difficult to construct a Hamiltonian path between two arbitrary nodes in a faulty WK-recursive network. In this paper, we show that K(d,t) is (d-4)-node Hamiltonian-connected. Since the connectivity of K(d,t) is d-1, the result is optimal in the worst case.     

Repetition-based cooperative broadcasting for vehicular ad-hoc networks

In vehicular ad hoc networks, most of critical applications involved with safety rely on reliable broadcast communications with low latency. Recently, repetition-based protocols have been proposed to meet the requirements of timeliness and reliability for broadcasting. In these protocols, a sender repeatedly retransmits the broadcast message during the lifetime of the message. However, existing protocols face serious problems such as deterioration of the signal quality caused by wireless fading. In particular, since excessive repetitions might cause network congestion and waste channel resources, reliability of broadcasting should be achieved with as small a number of repetitions as possible. In this paper, we therefore propose a novel repetition-based broadcast protocol which exploits a cooperative diversity technique (called RB-CD) making a small number of repetitions robust for wireless fading. To support this cooperative diversity, neighboring nodes transmit the same message almost simultaneously (that is, using the same repetition pattern for each other) in order to form a virtual antenna array. The virtual antenna array achieves a diversity gain at the receivers. In the RB-CD protocol, the virtual antenna array consists of the source and some of its neighbors (called relays) which participate in repeating the transmission of a broadcast message. In addition, a new distributed relay selection algorithm is introduced in the RB-CD protocol. From the ns-2 simulation results, we verified that RB-CD provides a more reliable broadcasting service due to its capability of exploiting cooperative diversity.     

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.     

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     

Efficient broadcasting in wormhole-routed multicomputers: anetwork-partitioning approach

In this paper, a network-partitioning approach for one-to-all broadcasting on wormhole-routed networks is proposed. To broadcast a message, the scheme works in three phases. First, a number of data-distributing networks (DDNs), which can work independently, are constructed. Then the message is evenly divided into submessages, each being sent to a representative node in one DDN. Second, the submessages are broadcast on the DDNs concurrently. Finally, a number of data-collecting networks (DCNs), which can work independently too, are constructed. Then, concurrently on each DCN, the submessages are collected and combined into the original message. Our approach, especially designed for wormhole-routed networks, is conceptually similar but fundamentally very different from the traditional approach of using multiple edge-disjoint spanning trees in parallel for broadcasting in store-and-forward networks. One interesting issue is on the definition of independent DDNs and DCNs, in the sense of wormhole routing. We show how to apply this approach to tori, meshes, and hypercubes. Thorough analyses and comparisons based on different system parameters and configurations are conducted. The results do confirm the advantage of our scheme, under various system parameters and conditions, over other existing broadcasting algorithms     

Topological Properties of WK-Recursive Networks

The WK-recursive networks, which have been proposed by Vecchia and Sanges, offer high degree of regularity, scalability, and symmetry. They have also the properties of expansibility and equal degree. Many algorithmic results have been obtained for the WK-recursive networks, and a VLSI implementation of a 16-node WK-recursive network has been realized. In this paper, we investigate some topological properties of the WK-recursive networks, including container, wide diameter, and fault diameter.     

An Adaptive Routing Algorithm for WK-Recursive Topologies

This paper presents an easy and straightforward routing algorithm for WK-recursive topologies. The algorithm, based on adaptive routing, takes advantage of the geometric properties of such topologies. Once a source node S and destination node D have been determined for a message communication, they characterize, at some level l, two virtual nodes and that respectively contain S but not D and D but not S. Such virtual nodes characterize other (where is the node degree for a fixed topology) virtual nodes of the same level that contain neither S nor D. Consequently, it is possible to locate triangles whose vertices are these virtual nodes with property to share the same path, called the self-routing path, directly connecting to . When the self-routing path is unavailable to transmit a message from S to D because of deadlock, fault, and congestion conditions, the routing strategy can follow what we call the triangle rule to deliver it. The proposed communication scheme has the advantage that 1) it is the same for all three conditions; 2) each node of a WK-recursive network, to transmit messages, does not require any information about their presence or location. Furthermore, this routing algorithm is able to tolerate up to faulty links. Received: July 19, 1998; revised May 17, 1999     

Parallel routing algorithms for incomplete hypercube interconnection networks

Hypercube interconnection networks have been receiving considerable attention in the supercomputing environment. However, the number of processors must be exactly 2^r for an r-cube complete hypercube. This restriction severely limits its applicability. In this paper, we address three variant hypercube topologies with more flexibility in system sizes, the labelled hypercubes I_m^r, I_M^r, and I_A^r. Incomplete hypercube I_m^r consists of an r-cube and an m-cube complete hypercubes; I_m^r is composed of 2^r and Σ_{m ε M} 2^m nodes; I_Ar comes from an r-cube complete hypercube which operates in a degraded manner and allows that the missing nodes to be arbitrarily distributed. Specifically, we focus on the parallel paths routing algorithms for these three classes of incomplete hypercubes. Parallel paths between any given two nodes mean that these paths have the same source and destination nodes but with different intermediate nodes. Parallel communication is important as it will allow us to use the full bandwidth of the multiprocessors for the data transfer operation between any two nodes, and3these redundant paths can increase system fault-tolerance and communication reliability. With these parallel routing algorithms, one can use them as a criterion to design multiprocessor systems.     

节点度估计和静态博弈转发策略的Ad Hoc网络路由协议

针对Ad Hoc网络路由发现过程中广播路由请求分组导致的广播风暴问题，提出了一种基于节点度估计和静态博弈转发策略的Ad Hoc网络路由协议NGRP.NGRP考虑边界影响，采用分段函数的思想将网络场景分为中心、边和角区域，分别估算网络中节点在不同区域的节点度，避免了周期性广播Hello消息获取节点度导致的开销；NGRP路由请求分组的转发采用静态博弈转发策略，利用节点度估算参与转发路由请求分组的节点数量，将转发和不转发作为策略集合，设计效益函数，通过纳什均衡获得节点转发路由请求分组的转发概率，从而减少了路由请求分组广播过程中产生的大量的冗余、竞争和冲突，提高了路由发现过程中路由请求分组的广播效率.运用NS-2对协议的性能进行大量的仿真，结果表明：NGRP的分组投递率、路由开销、MAC层路由开销和吞吐率这4项指标明显优于AODV+FDG，AODV with Hello和AODV without Hello协议.     

基于秘密共享的无线传感器网络广播密钥分发协议

在无线传感器网络中,能量消耗主要集中在节点之间的通信上,节点计算所消耗的能量远小于通信所消耗的能量。由于无线传感器网络的"一对多"和"多对一"通信模式,广播是节约能量的主要通信方式。为了保证广播实体和消息的合法性和保密性,必须首先解决无线传感器网络广播密钥安全分发问题。本文在充分考虑无线传感器网络自身特点的基础上,基于Shamir的门限秘密共享方案,提出了椭圆曲线双线性对上的无线传感器网络广播密钥分发协议,并对其进行安全性和性能分析。分析发现,该协议不仅满足安全性要求,同时,能够适合无线传感器网络的特殊应用要求。     

Sparse structures for searching and broadcasting algorithms over internet graphs and peer-to-peer computing systems

In a broadcasting problem, a message is sent from a source to all the other nodes in the network. Blind flooding is a classical mechanism for broadcasting, where each node retransmits received message to all its neighbors. Despite its important advantages, an increase in the number of requests or the network size or density produces communication overheads that limit the scalability of blind flooding, especially in networks with dynamic topologies. Theoretically optimal solution is based on minimal spanning trees (MST), but its construction is expensive. We discuss here protocols based on local knowledge and newly proposed sparse structures. In weighted RNG (Relative Neighborhood Graph), messages are forwarded only on links which are not the ‘longest’ in any triangle. In weighted RNGQ, messages are forwarded to links which are not the longest in any triangle or quadrangle. Each node constructs weighted MST based on its 2-hop knowledge. Weighted LMST (Localized LMST) preserves only edges that are selected by both endpoints, and messages are forwarded on these links. Any available metric, such as delay, reliability, reputation etc. can be used as weight. Analysis and simulation show that weighted RNG performs better than existing Flooding and Rumor Mongering (or Gossip) schemes. The parameterless weighted LMST, MST, RNG and RNGQ (RNG over Quadrangle) based broadcasting schemes are compared, showing overall advantage for LMST. We also hint that a number of existing protocols can be simplified by applying concept from this article.