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

TLDR

Fault‑tolerance measures for multiprocessor systems have traditionally assumed that any subset of components may fail simultaneously, and prior algorithms for assessing connectivity required O(n·2^(n−1)) steps. This work generalizes those measures by limiting the potentially faulty sets to specific subsets of system components. The author presents an O(k n/4)‑time algorithm to test connectivity for up to 2n−2 faulty processors, and applies it to n‑cube networks under the constraint that no two adjacent processors fail simultaneously. The analysis demonstrates that n‑cube networks can tolerate up to 2n−3 processor failures while remaining connected, and that the network diameter increases by at most a constant.

Abstract

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<or=2n-2, is given. The previously known algorithms for the same purpose require O(n*2/sup n-1/) computation steps.<<ETX>>