A Linear Time Pessimistic Diagnosis Algorithm for Hypermesh Multiprocessor Systems under the PMC Model

In microprocessor-based systems, such as the cloud computing infrastructure, high reliability is essential. As multiprocessor systems become more widespread and increasingly complex, system-level diagnosis will increasingly be adopted to determine their robustness. In this paper, we consider a pessimistic diagnostic strategy for hypermesh multiprocessor systems under the PMC model. The pessimistic strategy is a diagnostic process whereby all faulty processors are correctly identified and at most one fault-free processor may be misjudged to be a faulty processor. We first determine the pessimistic diagnosability of a hypermesh to be
${2}{{n}}({{k}} - {1}) - {{k}}$
. We then propose an efficient pessimistic diagnostic algorithm to identify at most
${ 2}{{n}}({{k}} - { 1}) - {{k}}$
faults in
${{O}}({{N}})$
time, where
${\mbi{k}}$
is the radix,
${\mbi{n}}$
is the number of dimensions, and
${{N}} = {{k^n}}$
is the total number of processors. This result is superior to the best precise diagnostic algorithm, which runs in
${{O}}({{N}}{\log _{{k}}}{{N}})$
time. Furthermore, the Cartesian product network, a subgraph of the hypermesh and the proposed algorithm can be employed to determine faults in the product network.