In developing deterministic measures of system-level fault tolerance for multiple-processor systems, it has generally been assumed that any subset of system components (processors or links) can potentially fail at the same time. In the present work, the author generalizes these measures by restricting the potentially faulty sets to some subsets of the system components. Using this model, he presents a fault-tolerance analysis for the n-cube networks that shows that such networks can tolerate up to 2n-3 processor failures and remain connected provided that for each processor p in the network, all the processors which are directly connected to p do not fail at the same time. He also shows that in this situation the diameter of the network may increase only by a constant value. The author presents an O((kn)/sup 2/) time algorithm for determining if the network is disconnected when a set of k faulty processors, k >

Generalized measures of fault tolerance with application to N-cube networks

Diagnosability has played an important role in the reliability of an interconnection network. The classical problem of fault diagnosis is discussed widely and the diagnosability of many well-known networks have been explored. We introduce a new measure of diagnosability, called conditional diagnosability, by restricting that any faulty set cannot contain all the neighbors of any vertex in the graph. Based on this requirement, the conditional diagnosability of the n-dimensional hypercube is shown to be 4(n - 2) +1, which is about four times as large as the classical diagnosability. Besides, we propose some useful conditions for verifying if a system is t-diagnosable and introduce a new concept, called a strongly t-diagnosable system, under the PMC model. Applying these concepts and conditions, we investigate some t-diagnosable networks which are also strongly t-diagnosable.

https://ir.nctu.edu.tw:443/bitstream/11536/14020/1/000225715900008.pdf

Conditional diagnosability measures for large multiprocessor systems

Fault- tolerant characteristics of a Boolean n cube array of microprocessors are analyzed. Connectivity properties of the network graph are used to show that n processor or link failures are required to isolate a processor. For processor failures the network is shown to be n (one step) diagnosable. A testing algorithm is presented which can diagnose up to n processor failures.

Fault Diagnosis in a Boolean n Cube Array of Microprocessors

Processor fault diagnosis takes an important role in fault-tolerant computing on multiprocessor systems. There are two classical diagnosis strategies - the precise strategy and the pessimistic strategy, both of which are based on the well-known PMC diagnostic model. Nevertheless, the degree of diagnosability of the system is limited under these two strategies. A better method, called the t/k-diagnosis strategy, is proposed by Somani and Peleg, in which the identified fault-set is allowed to contain at most k fault-free processors. Using this diagnosis strategy, the degree of diagnosability of the hypercube increases greatly as the number of the fault-free processors in the fault-set increases. We study the t/k-diagnosability of so-called BC graphs that include hypercubes, crossed cubes, Mobius cubes, and twisted cubes, etc. We show that any n-dimensional BC graph is t(n, k)/k-diagnosable when n/spl ges/4 and 0/spl les/k/spl les/n, where t(n,k)=(k+1)n-1/2(k+1)(k+2)+1. Therefore, the crossed cube, the Mobius cube, and the twisted cube all have the same t/k-diagnosability as the hypercube. As a result, the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on BC graphs.

The t/k-diagnosability of the BC graphs

A new class of modular networks is proposed for hierarchically constructing massively parallel computer systems for distributed supercomputing and AI applications. These networks are called hypernets. They are constructed incrementally with identical cubelets, treelets, or buslets that are well suited for VLSI implementation. Hypernets integrate positive features of both hypercubes and tree-based topologies, and maintain a constant node degree when the network size increases. This paper presents the principles of constructing hypernets and analyzes their architectural potentials in terms of message routing complexity, cost-effective support for global as well as localized communication, I/O capabilities, and fault tolerance. Several algorithms are mapped onto hypernets to illustrate their ability to support parallel processing in a hierarchically structured or data-dependent environment. The emulation of hypercube connections using less hardware is shown. The potential of hypernets for efficient support of connectionist models of computation is also explored.

Hypernet: A Communication-Efficient Architecture for Constructing Massively Parallel Computers

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Fault Diagnosis in a Boolean n Cube Array of Microprocessors