Routing permutations with link-disjoint and node-disjoint paths in a class of self-routable interconnects

We consider efficiently routing permutations in a class of switch-based interconnects. Permutation is an important communication pattern in parallel and distributed computing systems. We present a generic approach to realizing arbitrary permutations in a class of unique-path, self-routable interconnects. It is well-known that this type of interconnect has low hardware cost, but can realize only a small portion of all possible permutations between its inputs and outputs in a single pass. We consider routing arbitrary permutations with link-disjoint paths and node-disjoint paths in such interconnects in a minimum number of passes. In particular, routing with node-disjoint paths has important applications in emerging optical interconnects. We employ and further expand the Latin square technique used in all-to-all personalized exchange algorithms for this class of interconnects for general permutation routing. Our implementation of permutation routing is optimal in terms of the number of passes that messages are transmitted through the network, and it is near-optimal in network transmission time for sufficiently long messages. The possibility of adopting a single-stage interconnect is also discussed.     

Guaranteed on-demand discovery of node-disjoint paths in ad hoc networks

In recent years, the low cost and abundance of WLAN products has led to the deployment of self-configuring multihop ad hoc networks. Multipath routing has been increasingly studied to improve network reliability and throughput. However, no existing work guarantees discovery of node-disjoint paths when they exist, which limits their applicability in real networks. This paper presents a theoretical framework that establishes the equivalence between multipath discovery and flow network assignment. This equivalence is used to guarantee the on-demand discovery of an arbitrary number of node-disjoint paths between a pair of nodes as long as they exist. We also present an example protocol that integrates the theoretical framework with the Dynamic Source Routing (DSR) protocol to find two node-disjoint paths, which can be easily extended to finding k node-disjoint paths. Analysis of the example protocol demonstrates a good tradeoff between complexity and capability, particularly when compared with existing on-demand multipath routing protocols. Our simulation data shows the effectiveness of the discovered paths.     

Fault-tolerant routing over shortest node-disjoint paths in hypercubes

This paper presented a routing algorithm that finds n disjoint shortest paths from the source node s to target node d in the n-dimensional hypercube. Fault-tolerant routing over all shortest node-disjoint paths has been investigated to overcome the failure encountered during routing in hypercube networks. In this paper, we proposed an efficient approach to provide fault-tolerant routing which has been investigated on hypercube networks. The proposed approach is based on all shortest node-disjoint paths concept in order to find a fault-free shortest path among several paths provided. The proposed algorithm is a simple uniform distributed algorithm that can tolerate a large number of process failures, while delivering all n messages over optimal-length disjoint paths. However, no distributed algorithm uses acknowledgement messages (acks) for fault tolerance. So, for dealing the faults, acknowledgement messages (acks) are included in the proposed algorithm for routing messages over node-disjoint paths in a hypercube network.     

An efficient construction of one-to-many node-disjoint paths in folded hypercubes

A folded hypercube is basically a hypercube with additional links augmented, where the additional links connect all pairs of nodes with longest distance in the hypercube. In an n$n$-dimensional folded hypercube, it has been shown that n+1$n+1$ node-disjoint paths from one source node to other n+1$n+1$ (mutually) distinct destination nodes, respectively, can be constructed in O(n⁴)$O\left(n^4\right)$ time so that their maximal length is not greater than ⌈n/2⌉+1$\lceil n/2\rceil +1$, where n+1$n+1$ is the connectivity and ⌈n/2⌉$\lceil n/2\rceil$ is the diameter. Besides, their maximal length is minimized in the worst case. In this paper, we further show that by minimizing the computations of minimal routing functions, these node-disjoint paths can be constructed in O(n³)$O\left(n^3\right)$ time, which is more efficient, and is hard to be reduced because it must take O(n³)$O\left(n^3\right)$ time to compute a minimal routing function by solving a corresponding maximum weighted bipartite matching problem with the best known algorithm.     

Routing multiple paths in hypercubes

We present new techniques for mapping computations onto hypercubes. Our methods speed up classical implementations of grid and tree communications by a factor of (n), wheren is the number of hypercube dimensions. The speedups are asymptotically the best possible.We obtain these speedups by mapping each edge of the guest graph onto short, edge-disjoint paths in the hypercube such that the maximum congestion on any hypercube edge isO(1). These multiple-path embeddings can be used to reduce communication time for large grid-based scientific computations, to increase tolerance to link faults, and for fast routing of large messages.We also develop a general technique for deriving multiple-path embeddings from multiple-copy embeddings. Multiple-copy embeddings are one-to-one maps of independent copies of the guest graph within the hypercube. We present an efficient multiple-copy embedding of the cube-connected-cycles network within the hypercube. This embedding is used to derive efficient multiple-path embeddings of trees and butterfly networks in hypercubes.This research was supported by NSF/DARRA Grant CCR-8908285, NSF Grant CCR-8807426, and AFOSR Grant 89-0382.     

移动自组网中基于相关因子的多路径节能路由算法

一方面,由于移动自组网节点的能量由电池供应,一旦能量耗尽,不能继续充电,使用多路径可以节省能源;另一方面,使用多路径即便是节点不相交多路径,由于移动自组网的无线多播特性,仍存在严重的冲突问题。综合这两方面因素,提出了冲突受限的节能路由算法。该算法引入相关因子来衡量多路径同时进行数据传输时发生冲突的可能性,然后根据特定应用对传输性能的要求,得到一个冲突上限,即相关因子的最大值,最后找到能满足冲突上限的最节能的一组节点不相交多路径。仿真结果表明,该算法与单纯的节能路由算法——源传输功率选择算法（STPS）相比,可显著降低数据传输时的丢包率,且没有明显增加能量消耗和寻路时间。     

Performing permutations on interconnection networks by regularlychanging switch states

In this paper, we present an algorithm for performing permutations of messages on multistage interconnection networks. Permutations of messages are needed in many parallel algorithms. The proposed algorithm is feasible for any networks that can connect each input to each output using a set of N nonblocking connections, where N is the number of ports on the network. Messages are segmented into N submessages that are sent independently in each time step. For any permutation, the settings of switches are changed with fixed patterns. Partitioning of the network into independent subnetworks is also supported, each capable of simultaneously routing a different permutation     

蜂窝网络上的路由算法*

主要研究蜂窝网络上的无死锁单播路由算法和一对全的广播路由算法。基于蜂窝网络的砖形画法,利用二维网络维序路由的基本思想和两个虚拟网络实现了无死锁的最短单播路由算法,并证明了算法的无死锁性。然后基于这个单播路由算法和线列上的广播算法,用软件实现了蜂窝网络上一对全的广播路由算法,经过简单比较得出该广播算法比以往的算法在通信效率上有了极大的提高。     

Routing with admission control in ATM networks

An optimal control parameter, , was developed by optimal control theory for Asynchronous Transfer Mode (ATM) networks. The parameter is related to link utilization, buffer occupancy, system throughput and cell rejection characteristics and is applied to routing and admission control in simulation of a network carrying multiclass traffic. Simulation results show that the parameter produces better performance with respect to cell rejection rate characteristics compared with the traditional control parameter for utilization, .This research has been supported by the ATI as part of the Navy Contract N00140-94-C-BC03. Some parts of the paper were presented at Globecom'94.     

具有自适应性的star网络容错寻径策略研究

大规模并行处理机系统中寻径算法对互连网络的通信性能和系统性能起着至关重要的作用,而star互连网络作为超立方体网络的最好替代之一,其寻径问题的解决变得非常重要。在有条件的容错模型基础上,对寻径时的规则进行了研究,提出了一种基于自适应规则的容错寻径算法。对算法的正确性以及容错性进行了分析。经仿真实验证明了该算法具有较高的成功概率。在边失效独立的情况下,对star网络终端对间通信可靠性进行了分析,推导出了其约束下界,并给予了证明。     

Shortest paths in stochastic networks with correlated link costs

The objective is to minimize expected travel time from any origin to a specific destination in a congestible network with correlated link costs. Each link is assumed to be in one of two possible conditions. Conditional probability density functions for link travel times are assumed known for each condition. Conditions over the traversed links are taken into account for determining the optimal routing strategy for the remaining trip. This problem is treated as a multistage adaptive feedback control process. Each stage is described by the physical state (the location of the current decision point) and the information state (the service level of the previously traversed links). Proof of existence and uniqueness of the solution to the basic dynamic programming equations and a solution procedure are provided.     

Ad hoc网络中一种带预测的路由算法

在自组网中,由于网络节点的移动性及拓扑结构的易变性,设计稳定的路由成为最受关注的问题。根据可靠性为多路径路由选择更多的可靠路径,以满足自组网中多路径传输在路径的数量和质量方面的需求,是多路径路由技术中的一个重要研究课题。为此,基于GRID模型和预测模型提出了一种带预测的稳定不相交备用路由算法,其利用有效限制路由查询包的泛洪区域,并结合预测策略和节点不相交路径算法来选择一条最稳定的不相交备用路由,从而进一步提高该路由算法的性能。模拟结果显示,与其他3个多路径路由相比较,该算法是一个有效的自组网路由算法。     

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.     

Node-disjoint paths in hierarchical hypercube networks

The hierarchical hypercube network is suitable for massively parallel systems. One of its appealing properties is the low number of connections per processor, which can facilitate the VLSI design and fabrication. Other alluring features include symmetry and logarithmic diameter, which can derive easy and fast algorithms for communication. In this paper, a maximal number of node-disjoint paths are constructed between every two distinct nodes of the hierarchical hypercube network. Their maximal length is not greater than max{2^m+1+2m+1,2^m+1+m+4}, where 2^m+1 is the diameter. The effectiveness of node-disjoint paths is further verified by experiments.     

The design of complete encryption networks using cryptographically equivalent permutations

A design procedure for complete substitution-permutation encryption networks is presented. The cryptographically important property of completeness is achieved after three iterations, the minimum possible number for all networks of size N = i · n² (i = 1,2,…,n), where n is the size of the substitution function used. The permutation stage is constructed by choosing a single member of a class of cryptographically equivalent permutations for all the network rounds, hence having the advantage of simplifying the network implementation. An algorithm for generating members of the class of cryptographically equivalent permutations is given.     

机会网络路由协议

在机会网络中由于网络稀疏、节点移动和通信范围等因素的影响,有可能出现网络分裂或节点脱网,源节点和目的节点之间不一定存在完整的端到端路径,这为路由协议的设计带来巨大挑战,此问题近年来引起了研究人员越来越多的关注。首先介绍了机会网络的基本概念、体系结构和特点等;然后阐述了机会网络路由协议研究的进展,概括了机会网络路由协议中的新机制,对现有路由协议进行分类并详述它们的基本原理;通过比较对各种协议的特点进行分析阐述,最后给出未来研究的方向。     

Routing in sparse splitting optical networks with multicast traffic

In this paper, we investigate the problem of Multicast Routing in Sparse Splitting Networks (MR-SSN). Given a network topology with the multicast capable nodes distributed uniformly throughout the network, and a multicast session, the MR-SSN problem is to find a route from the source node of the multicast session to all destinations of the multicast session such that the total number of fibers used in establishing the session is minimized. In this paper, we develop a rerouting algorithm for a given Steiner tree, which makes it feasible to route a multicast session using a tree-based solution in sparse light splitting optical networks. In addition, we present a heuristic based on Tabu Search (TS) that requires only one transmitter for the source node and one wavelength for each multicast session. To evaluate the performance of heuristics, we formulate the MR-SSP problem as an integer linear program (ILP), and optimally solve small instances using the commercially available linear solver, CPLEX. We test our heuristic on a wide range of network topologies. Our experimental results show that: (1) The difference between our solution and ILP optimal solution, in terms of the number of fibers used for establishing a multicast session, is within 10% in almost all the instances and within 5% in about half of the instances. (2) The average delay, taken over all destination nodes, falls within three times the optimal value. (3) A sparse light splitting all-optical network with 30% of multicast capable cross-connects has an acceptable low cost and relatively good performance. (4) The improvement achieved by TS heuristic increases considerably when the session size is large, the number of Splitter-and-Delivery cross-connects is small, and the network connectivity is dense.     

Routing in wormhole-switched clustered networks with applicationsto fault tolerance

This paper presents a novel technique for routing in wormhole-switched multiprocessor interconnection networks with clustered configuration. The network model used here consists of a set of clusters interfaced through a common central network. We assume that the central network and the clusters use independent algorithms to route messages between their internal nodes. A technique for deriving a global routing algorithm based on the local algorithms is presented, which allows the transfer of messages between any pair of nodes in the network. This proposed method is shown to be deadlock-free with two virtual channels. The clustered network model and the proposed routing technique can be used to enhance the fault tolerance capability of existing routing algorithms. In particular, we describe fault-tolerant routing methods for meshes, which can tolerate any arbitrary fault distribution without disabling connected healthy nodes