Self-stabilizing wormhole routing in hypercubes

Wormhole routing is an efficient technique used to communicate message packets between processors when they are not completely connected. To the best of our knowledge, this is the first attempt at designing a self-stabilizing wormhole routing algorithm for hypercubes. Our first algorithm handles all types of faults except for node/link failures. This algorithm achieves optimality in terms of routing path length by following only the preferred dimensions. In an n-dimensional hypercube, those dimensions in which source and destination address bits differ are called preferred dimensions. Our second algorithm handles topological changes. We propose an efficient scheme of rerouting flits in case of node/link failures. Similar to the first algorithm, this algorithm also tries to follow preferred dimensions if they are nonfaulty at the time of transmitting the flits. However, due to topological faults it is necessary to take non-preferred dimensions resulting in suboptimality of path selection. Formal proof of correctness for both solutions is given. (Abstract shortened by UMI.)

Compact routing in fault-tolerant distributed systems

A compact routing algorithm is a routing algorithm which reduces the space complexity of all-pairs shortest path routing. Compact routing protocols in distributed systems have been studied extensively as an attractive alternative to the traditional method of all-pairs shortest path routing. The use of compact routing protocols have several advantages. Compact routing schemes are not only more memory-efficient, but provide faster routing table lookup, more efficient broadcast scheme, and allow for a more scalable network. These routing schemes still maintain optimal or near-optimal routing paths. However, most of the compact routing protocols are not fault-tolerant. This thesis will first report the recent developments in the compact routing research. Several new methods for compact routing in fault-tolerant distributed systems will be presented and analyzed. The most important feature of the algorithms presented in this thesis is that they are self-stabilizing. The self-stabilization paradigm has been shown to be the most unified and all-inclusive approach to the design of fault-tolerant system. Additionally, these algorithms will address and solve several problems left unsolved by previous works. Relabelable and non-relabelable networks will be considered for both specific and arbitrary topologies

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}

Recursive Cube of Rings: A new topology for interconnection networks

In this paper, we introduce a family of scalable interconnection network topologies, named Recursive Cube of Rings (RCR), which are recursively constructed by adding ring edges to a cube. RCRs possess many desirable topological properties in building scalable parallel machines, such as fixed degree, small diameter, wide bisection width, symmetry, fault tolerance, etc. We first examine the topological properties of RCRs. We then present and analyze a general deadlock-free routing algorithm for RCRs. Using a complete binary tree embedded into an RCR with expansion-cost approximating to one, an efficient broadcast routing algorithm on RCRs is proposed. The upper bound of the number of message passing steps in one broadcast operation on a general RCR is also derived.published_or_final_versio

Processor allocation strategies for modified hypercubes

Parallel processing has been widely accepted to be the future in high speed computing. Among the various parallel architectures proposed/implemented, the hypercube has shown a lot of promise because of its poweful properties, like regular topology, fault tolerance, low diameter, simple routing, and ability to efficiently emulate other architectures. The major drawback of the hypercube network is that it can not be expanded in practice because the number of communication ports for each processor grows as the logarithm of the total number of processors in the system. Therefore, once a hypercube supercomputer of a certain dimensionality has been built, any future expansions can be accomplished only by replacing the VLSI chips. This is an undesirable feature and a lot of work has been under progress to eliminate this stymie, thus providing a platform for easier expansion. Modified hypercubes (MHs) have been proposed as the building blocks of hypercube-based systems supporting incremental growth techniques without introducing extra resources for individual hypercubes. However, processor allocation on MHs proves to be a challenge due to a slight deviation in their topology from that of the standard hypercube network. This thesis addresses the issue of processor allocation on MHs and proposes various strategies which are based, partially or entirely, on table look-up approaches. A study of the various task allocation strategies for standard hypercubes is conducted and their suitability for MHs is evaluated. It is shown that the proposed strategies have a perfect subcube recognition ability and a superior performance. Existing processor allocation strategies for pure hypercube networks are demonstrated to be ineffective for MHs, in the light of their inability to recognize all available subcubes. A comparative analysis that involves the buddy strategy and the new strategies is carried out using simulation results

Interconnection Networks Embeddings and Efficient Parallel Computations.

To obtain a greater performance, many processors are allowed to cooperate to solve a single problem. These processors communicate via an interconnection network or a bus. The most essential function of the underlying interconnection network is the efficient interchanging of messages between processes in different processors. Parallel machines based on the hypercube topology have gained a great respect in parallel computation because of its many attractive properties. Many versions of the hypercube have been introduced by many researchers mainly to enhance communications. The twisted hypercube is one of the most attractive versions of the hypercube. It preserves the important features of the hypercube and reduces its diameter by a factor of two. This dissertation investigates relations and transformations between various interconnection networks and the twisted hypercube and explore its efficiency in parallel computation. The capability of the twisted hypercube to simulate complete binary trees, complete quad trees, and rings is demonstrated and compared with the hypercube. Finally, the fault-tolerance of the twisted hypercube is investigated. We present optimal algorithms to simulate rings in a faulty twisted hypercube environment and compare that with the hypercube

Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability