Efficient embedding of virtual hypercubes in irregular WDM optical networks

This thesis addresses one of the important issues in designing future WDM optical networks. Such networks are expected to employ an all-optical control plane for dissemination of network state information. It has recently been suggested that an efficient control plane will require non-blocking communication infrastructure and routing techniques. However, the irregular nature of most WDM networks does not lend itself to efficient non-blocking communications. It has been recently shown that hypercubes offer some very efficient non-blocking solutions for, all-to-all broadcast operations, which would be very attractive for control plane implementation. Such results can be utilized by embedding virtual structures in the physical network and doing the routing using properties of a virtual architecture. We will emphasize the hypercube due to its proven usefulness. In this thesis we propose three efficient heuristic methods for embedding a virtual hypercube in an irregular host network such that each node in the host network is either a hypercube node or a neighbor of a hypercube node. The latter will be called a “satellite” or “secondary” node. These schemes follow a step-by-step procedure for the embedding and for finding the physical path implementation of the virtual links while attempting to optimize certain metrics such as the number of wavelengths on each link and the average length of virtual link mappings. We have designed software that takes the adjacency list of an irregular topology as input and provides the adjacency list of a hypercube embedded in the original network. We executed this software on a number of irregular networks with different connectivities and compared the behavior of each of the three algorithms. The algorithms are compared with respect to their performance in trying to optimize several metrics. We also compare our algorithms to an already existing algorithm in the literature

Hamiltonian Decompositions of Regular Topology Networks with Convergence Routing

This paper introduces new methods to construct multiple virtual rings for loss-free routing of non-reserved bursty data in high-speed environments such as ATM LANs. The routing algorithm on multiple virtual rings is convergence routing which combines the actual routing decision with the internal flow control state. Multiple virtual rings are obtained on the hypercube and the circulant networks such that each virtual ring is hamiltonian, and are mutually edge-disjoint. It is shown that multiple virtual rings improve (i) the bound on the length of routing, and (ii) the fault tolerance. On the circulant graphs, necessary and sufficient conditions for hamiltonian decomposition is established. On the hypercube, three algorithms are designed for an N-node hypercube with even dimension: (i) an O(N) time algorithm to find two edge-disjoint hamiltonian circuits, (ii) an O(N log N) time algorithm to find I01N hamiltonian circuits with only E ~ 0.1 common edges, and (iii) a recursive algorithm for the hamiltonian decomposition of the hypercube with dimension power of two. It is shown analytically, and verified by simulations on the circulants that with the d virtual ring embeddings, a bound of O( N / d) is established on the maximum length of routing

Embedding cube-connected cycles graphs into faulty hypercubes

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults

Redundancy management for efficient fault recovery in NASA's distributed computing system

The management of redundancy in computer systems was studied and guidelines were provided for the development of NASA's fault-tolerant distributed systems. Fault recovery and reconfiguration mechanisms were examined. A theoretical foundation was laid for redundancy management by efficient reconfiguration methods and algorithmic diversity. Algorithms were developed to optimize the resources for embedding of computational graphs of tasks in the system architecture and reconfiguration of these tasks after a failure has occurred. The computational structure represented by a path and the complete binary tree was considered and the mesh and hypercube architectures were targeted for their embeddings. The innovative concept of Hybrid Algorithm Technique was introduced. This new technique provides a mechanism for obtaining fault tolerance while exhibiting improved performance

Simulation of Meshes in a Faulty Supercube with Unbounded Expansion

[[abstract]]Reconfiguring meshes in a faulty Supercube is investigated in the paper. The result can readily be used in the optimal embedding of a mesh (or a torus) of processors in a faulty Supercube with unbounded expansion. There are embedding algorithms proposed in this paper. These embedding algorithms show a mesh with any number of nodes can be embedded into a faulty Supercube with load 1, congestion 1, and dilation 3 such that O(n2-w2) faults can be tolerated, where n is the dimension of the Supercube and 2w is the number of nodes of the mesh. The meshes and hypercubes are widely used interconnection architectures in parallel computing, grid computing, sensor network, and cloud computing. In addition, the Supercubes are superior to hypercube in terms of embedding a mesh and torus under faults. Therefore, we can easily port the parallel or distributed algorithms developed for these structuring of mesh and torus to the Supercube.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]KO

Fault-Tolerant Ring Embeddings in Hypercubes -- A Reconfigurable Approach

We investigate the problem of designing reconfigurable embedding schemes for a fixed hypercube (without redundant processors and links). The fundamental idea for these schemes is to embed a basic network on the hypercube without fully utilizing the nodes on the hypercube. The remaining nodes can be used as spares to reconfigure the embeddings in case of faults. The result of this research shows that by carefully embedding the application graphs, the topological properties of the embedding can be preserved under fault conditions, and reconfiguration can be carried out efficiently. In this dissertation, we choose the ring as the basic network of interest, and propose several schemes for the design of reconfigurable embeddings with the aim of minimizing reconfiguration cost and performance degradation. The cost is measured by the number of node-state changes or reconfiguration steps needed for processing of the reconfiguration, and the performance degradation is characterized as the dilation of the new embedding after reconfiguration. Compared to the existing schemes, our schemes surpass the existing ones in terms of applicability of schemes and reconfiguration cost needed for the resulting embeddings

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified

Fault-tolerance embedding of rings and arrays in star and pancake graphs

The star and pancake graphs are useful interconnection networks for connecting processors in a parallel and distributed computing environment. The star network has been widely studied and is shown to possess attactive features like sublogarithmic diameter, node and edge symmetry and high resilience. The star/pancake interconnection graphs, {dollar}S\sb{n}/P\sb{n}{dollar} of dimension n have n! nodes connected by {dollar}{(n-1).n!\over2}{dollar} edges. Due to their large number of nodes and interconnections, they are prone to failure of one or more nodes/edges; In this thesis, we present methods to embed Hamiltonian paths (H-path) and Hamiltonian cycles (H-cycle) in a star graph {dollar}S\sb{n}{dollar} and pancake graph {dollar}P\sb{n}{dollar} in a faulty environment. Such embeddings are important for solving computational problems, formulated for array and ring topologies, on star and pancake graphs. The models considered include single-processor failure, double-processor failure, and multiple-processor failures. All the models are applied to an H-cycle which is formed by visiting all the ({dollar}{n!\over4!})\ S\sb4/P\sb4{dollar}s in an {dollar}S\sb{n}/P\sb{n}{dollar} in a particular order. Each {dollar}S\sb4/P\sb4{dollar} has an entry node where the cycle/path enters that particular {dollar}S\sb4/P\sb4{dollar} and an exit node where the path leaves it. Distributed algorithms for embedding hamiltonian cycle in the presence of multiple faults, are also presented for both {dollar}S\sb{n}{dollar} and {dollar}P\sb{n}{dollar}

Exploiting an alternative labeling for efficient hypercube algorithms

Ankara : Department of Computer Engineering and Information Science and Institute of Engineering and Sciences, Bilkent Univ., 1991.Thesis (Master's) -- Bilkent University, 1991.Includes bibliographical references leaves 57Aydın, CavitM.S