Reliability and Diagnosability Analysis of Hyper Bijective Connection Networks

Abstract

Bijective connection (BC) networks, including a family of interconnection networks of multiprocessor systems, have been studied extensively due to its desirable properties, such as lower diameter, high reliability, and diagnosability. To meet the demand of processing integrating tasks with large-scale and complex architectures, it is significant to explore alternative interconnection networks for multiprocessor configuration. To this end, we propose a novel framework called hyper bijective connection network (HBC network) as an extension of BC networks, which allows to study the properties of other potential interconnection networks in unity rather than in individual. We prove that when n ≥ 3, m ≥ 2, every n-dimensional HBC network H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (m) has (edge) connectivity m + n - 2, super connectivity 2n + m - 4, and super edge-connectivity 2n + 2m - 6, and is super-connected and super-edge-connected. These results indicate the high reliability of HBC networks. Moreover, we analyze three classic diagnos abilities of a HBC network, including tp-, t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -, and t/k-diagnosability. We show that when n ≥ 3 and m ≥ 2, an n-dimensional HBC network H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (m) is (m + n - 2)-diagnosable, (2n + m - 4)/(2n + m - 4)-diagnosable, and t(m, n, k)/k-diagnosable, where 0 ≤ k ≤ m + n - 2 and t(m, n, k) = (k + 1)n + (m - 2) - ((k + 1)(k + 2)/2) + 1. Besides, it is shown that the corresponding properties for BC networks can be derived naturally as special cases of that for HBC networks.