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Optimal Binomial Group Testing with a Test History

Published online by Cambridge University Press:  27 July 2009

B. Chen
Institute of Applied Mathematics, Beijing, China
X. D. Hu
Academia Sinica Beijing, China
F. K. Hwang
AT&T Bell Laboratories Murray Hill, New Jersey 07974


The classical binomial group-testing problem considers the use of a minimal number of group tests to identify all defectives in a set of items, each of which independently has probability p of being defective. The minimization problem is very difficult, and the only major result is that for p ≥ (3 - □ root;5) /2, Unger proved that one-by-one testing is the best. Recently, to study the complexity of the group-testing problem, researchers have considered the more general case in which the items have already been tested. Interestingly, Unger's result still holds in this case. However, since the items are no longer equivalent (nor independent), the sequencing of items of testing becomes a legitimate problem, one that did not arise in the classical case. In this paper, we give optimal sequencing under general conditions on the test history.

Copyright © Cambridge University Press 1990

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