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A Monotonicity Result for Inspecting Independent Items

Published online by Cambridge University Press:  27 July 2009

F.K. Hwang  and
S.G. Papastavridis
F.K. Hwang
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey 07974
S.G. Papastavridis
Affiliation:
Department of MathematicsUniversity of Patras, Greece
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Abstract

Recently, the conjecture that the expected number of tests is nondecreasing in the failure probability for binomial group testing has been proved. The proof has also been extended to three models of multiaccess systems. However, probabilistic algorithms are used as a crucial part of these proofs. In this paper, we give conceptually simpler new proofs without using probabilistic algorithms. We also extend the result to a more general model where the number of tests is replaced by a cost function.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 1 , January 1989 , pp. 135 - 140
Copyright
Copyright © Cambridge University Press 1989

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References

Hwang, F.K., Song, T.T. & Du, D.Z. (1981). Hypergeometric and generalized hypergeometric group testing. SIAM Journal on Algebraic and Discrete Methods 2: 426–428.CrossRefGoogle Scholar
Hwang, F.K. & Yao, Y.C. (1987). A generalization of the monotonicity theorem in group testing with applications to multiaccess channels. IEEE Transactions on Information Theory to appear.Google Scholar
Yao, Y.C. & Hwang, F.K. (1988). A fundamental monotonicity in group testing. SIAM Journal on Discrete Mathematics, 1: 256–259.CrossRefGoogle Scholar