Subcube embeddability and fault tolerance of augmented hypercubes

Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance. They are easily partitionable and exhibit a high degree of fault tolerance. Fault-tolerance in hypercube and hypercube-based networks received the attention of several researchers in recent years; The primary idea of this study is to address and analyze the reliability issues in hypercube networks. It is well known that the hypercube can be augmented with one dimension to replace any of the existing dimensions should any dimension fail. In this research, it is shown that it is possible to add i dimensions to the standard hypercube, Qn to tolerate (i - 1) dimension failures, where 0 \u3c i ≤ n. An augmented hypercube, Qn +(n) with n additional dimensions is introduced and compared with two other hypercube networks with the same amount of redundancy. Reliability analysis for the three hypercube networks is done using the combinatorial and Markov modeling. The MTTF values are calculated and compared for all three networks. Comparison between similar size hypercube networks show that the augmented hypercube is more robust than the standard hypercube; As a related problem, we also look at the subcube embeddability. Subcube embeddability of the hypercube can be enhanced by introducing an additional dimension. A set of new dimensions, characterized by the Hamming distance between the pairs of nodes it connects, is introduced using a measure defined as the magnitude of a dimension. An enumeration of subcubes of various sizes is presented for a dimension parameterized by its magnitude. It is shown that the maximum number of subcubes for a Qn can only be attained when the magnitude of dimension is n - 1 or n. It is further shown that the latter two dimensions can optimally increase the number of subcubes among all possible choices

Fault-tolerant meshes and hypercubes with minimal numbers of spares

Many parallel computers consist of processors connected in the form of a d-dimensional mesh or hypercube. Two- and three-dimensional meshes have been shown to be efficient in manipulating images and dense matrices, whereas hypercubes have been shown to be well suited to divide-and-conquer algorithms requiring global communication. However, even a single faulty processor or communication link can seriously affect the performance of these machines. This paper presents several techniques for tolerating faults in d-dimensional mesh and hypercube architectures. Our approach consists of adding spare processors and communication links so that the resulting architecture will contain a fault-free mesh or hypercube in the presence of faults. We optimize the cost of the fault-tolerant architecture by adding exactly k spare processors (while tolerating up to k processor and/or link faults) and minimizing the maximum number of links per processor. For example, when the desired architecture is a d-dimensional mesh and k = 1, we present a fault-tolerant architecture that has the same maximum degree as the desired architecture (namely, 2d) and has only one spare processor. We also present efficient layouts for fault-tolerant two- and three-dimensional meshes, and show how multiplexers and buses can be used to reduce the degree of fault-tolerant architectures. Finally, we give constructions for fault-tolerant tori, eight-connected meshes, and hexagonal meshes

Adaptive fault-tolerant routing in hypercube multicomputers

A connected hypercube with faulty links and/or nodes is called an injured hypercube. To enable any non-faulty node to communicate with any other non-faulty node in an injured hypercube, the information on component failures has to be made available to non-faulty nodes so as to route messages around the faulty components. A distributed adaptive fault tolerant routing scheme is proposed for an injured hypercube in which each node is required to know only the condition of its own links. Despite its simplicity, this scheme is shown to be capable of routing messages successfully in an injured hypercube as long as the number of faulty components is less than n. Moreover, it is proved that this scheme routes messages via shortest paths with a rather high probabiltiy and the expected length of a resulting path is very close to that of a shortest path. Since the assumption that the number of faulty components is less than n in an n-dimensional hypercube might limit the usefulness of the above scheme, a routing scheme is introduced based on depth-first search which works in the presence of an arbitrary number of faulty components. Due to the insufficient information on faulty components, the paths chosen by the above scheme may not always be the shortest. To guarantee that all messages be routed via shortest paths, it is proposed that every mode be equipped with more information than that on its own links. The effects of this additional information on routing efficiency are analyzed, and the additional information to be kept at each node for the shortest path routing is determined. Several examples and remarks are also given to illustrate the results

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

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

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.)