Probabilistic existence theorems in group testing |
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Institution: | Department of Statistics, School of Mathematics, Cardiff University, Senghennydd Road, P.O. Box 926 Cardiff CF24 4YH, UK |
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Abstract: | For a wide range of combinatorial group testing problems including additive, binary and multiaccess channel models, a probabilistic method is developed to derive upper bounds for the length of optimal nonsequential designs. A general result is proven allowing in many particular cases to compute the asymptotic bounds. The existence theorems are also derived for the situation when several errors in the test results can occur (searching with lies) and for the group testing problem in the binomial sample. |
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