On Adaptive Fault Diagnosis for Multiprocessor Systems
We first consider adaptive serial diagnosis for multiprocessor systems. We present an adaptive diagnosis algorithm using N+t.1 tests, which is the smallest possible number, for an N-processor system modeled by a (2t.1)-connected graph with at most t faulty processors. We also present an adaptive diagnosis algorithm using minimum number of tests for a system modeled by cube-connected cycles. We consider adaptive parallel diagnosis as well. We show that for adaptive parallel diagnosis of an N-processor system modeled by a hypercube, three testing rounds are necessary and suficient if the number of faulty processors is at most logN-⌈log(logN-⌈log logN⌉+4)⌉+2. We also show that three testing rounds are necessary and sufficient for adaptive parallel diagnosis of a system modeled by cube-connected cycles of dimension greater than three.
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