A universal bound for a covering in regular posets and its application to pool testing
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Application of cover-free codes and combinatorial designs to two-stage testing
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Generalized framework for selectors with applications in optimal group testing
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Noisy group testing: an information theoretic perspective
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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We adapt methods originally developed in information and coding theory to solve some testing problems. The efficiency of two-stage pool testing of n items is characterized by the minimum expected number E(n, p) of tests for the Bernoulli p-scheme, where the minimum is taken over a matrix that specifies the tests that constitute the first stage. An information-theoretic bound implies that the natural desire to achieve E(n, p) = o(n) as n → ∞ can be satisfied only if p(n) → 0. Using random selection and linear programming, we bound some parameters of binary matrices, thereby determining up to positive constants how the asymptotic behavior of E(n, p) as n → ∞ depends on the manner in which p(n) → 0. In particular, it is shown that for p(n) = n-β+o(1), where 0 < β < 1, the asymptotic efficiency of two-stage procedures cannot be improved upon by generalizing to the class of all multistage adaptive testing algorithms