Adaptive Diagnosis of Variants of the Hypercube

Aya OKASHITA  Toru ARAKI  Yukio SHIBATA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.3   pp.728-735
Publication Date: 2005/03/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.3.728
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Graphs and Networks
Keyword: 
system-level diagnosis,  adaptive diagnosis,  hypercube,  variants of hypercube,  parallel testing rounds,  

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Summary: 
System-level fault diagnosis deals with the problem of identifying faulty nodes (processors) in a multiprocessor system. Each node is faulty or fault-free, and it can test other nodes in the system, and outputs the test results. The test result from a node is reliable if the node is fault-free, but the result is unreliable if it is faulty. In this paper, we prove that four variants of the hypercube: the crossed cube, the twisted cube, the Mobius cube, and the enhanced cube, are adaptively diagnosed using at most 4 parallel testing rounds, with at most n faulty nodes (for the enhanced cube, with at most n + 1 faulty nodes), where each processor participates in at most one test in each round. Furthermore, we propose another diagnosis algorithm for the n-dimensional enhanced cube with at most n + 1 faulty nodes, and show that it is adaptively diagnosed with at most 5 rounds in the worst case, but with at most 3 rounds if the number of existing faulty nodes is at most n -log(n + 1).