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Almost Safe Group Testing with Few Tests†

Published online by Cambridge University Press:  12 September 2008

Andrzej Pelc
Andrzej Pelc
Affiliation:
Département d'Informatique, Université du Québec à Hull, C.P. 1250, succ. ‘B’, Hull, Québec J8X 3X7, Canada
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Abstract

In group testing, sets of data undergo tests that reveal if a set contains faulty data. Assuming that data items are faulty with given probability and independently of one another, we investigate small families of tests that enable us to locate correctly all faulty data with probability converging to one as the amount of data grows. Upper and lower bounds on the minimum number of such tests are established for different probability functions, and respective location strategies are constructed.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 3 , September 1994 , pp. 411 - 419
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Ahlswede, R. and Wegener, I. (1987) Search problems, Wiley and Sons, New York.Google Scholar
[2]Blough, D. M. and Pelc, A. (1994) Almost certain fault diagnosis through algorithm-based fault tolerance. IEEE Transactions on Parallel and Distributed Systems 5 532–539.CrossRefGoogle Scholar
[3]Dorfman, R. (1943) The detection of defective members of large populations. Ann. Math. Stat. 14 436–440.CrossRefGoogle Scholar
[4]Katona, G. (1973) Combinatorial search problems. In: Srivastava, et al. (eds.) A survey of combinatorial theory 285–308.CrossRefGoogle Scholar
[5]Nair, V., Hoskote, Y. and Abraham, J. (1992) Probabilistic evaluation of on-line checks in fault-tolerant multiprocessor systems. IEEE Transactions on Computers 41 532–541.CrossRefGoogle Scholar
[6]Sobel, M. (1960) Group testing to classify efficiently all defectives in a binomial sample. In: Machol, (ed.) Information and Decision Processes, McGraw-Hill, New York127–161.Google Scholar
[7]Sobel, M. (1968) Binomial and hypergeometric group testing. Studia Sci. Math. Hungar. 3 19–42.Google Scholar
[8]Sobel, M. and Groll, P. A. (1959) Group testing to classify efficiently all defectives in a binomial sample. Bell System Techn. J. 38 1179–1259.CrossRefGoogle Scholar
[9]Sterrett, A. (1957). On the detection of defective members of large populations. Ann. Math. Stat. 28 1033–1036.CrossRefGoogle Scholar