Locating faults in a constant number of parallel testing rounds
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Fault diagnosis in a small constant number of parallel testing rounds
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Probabilistic diagnosis of multiprocessor systems
ACM Computing Surveys (CSUR)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Reliable Fault Diagnosis with Few Tests
Combinatorics, Probability and Computing
IEEE Transactions on Computers
On Adaptive Fault Diagnosis for Multiprocessor Systems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Three-round adaptive diagnosis in binary n-cubes
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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We study adaptive system-level fault diagnosis for multiprocessor systems. Processors can test each other and later tests can be scheduled on the basis of previous test results. Fault-free testers correctly identify the fault status of tested processors, while faulty testers can give arbitrary test results. The goal is to identify correctly the status of all processors, assuming that the number of faults does not exceed a given upper bound t, where n is the number of processors. Tests involving disjoint pairs of processors can be performed simultaneously in one round. Two most important measures of quality of a diagnosis algorithm are its worst-case cost (the number of tests used) and time (the number of rounds used). It is known that the optimal worst-case cost of a diagnosis algorithm is n + t - 1. However, the known algorithms of this cost use time Θ(n). We present an algorithm with optimal cost n + t - 1 using time O(log t), provided that the upper bound t on the number of faults satisfies t(t + 1) ≤ n. Hence, for moderate numbers of faults which we assume, our algorithm achieves exponential speed-up, compared to the previously known diagnosis algorithms of optimal cost.