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arXiv · 0712.3876

Explicit Non-Adaptive Combinatorial Group Testing Schemes

Ely Porat·Amir Rothschild
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Abstract

Group testing is a long studied problem in combinatorics: A small set of $r$ ill people should be identified out of the whole ($n$ people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This scheme has $\bigT{\min[r^2 \ln n,n]}$ tests which is as many as the best non-explicit schemes have. In our construction we use a fact that may have a value by its own right: Linear error-correction codes with parameters $[m,k,δm]_q$ meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in $\bigT{q^km}$ time.

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Ely Porat, Amir Rothschild. 2008-04-29. Explicit Non-Adaptive Combinatorial Group Testing Schemes. https://arxiv.org/abs/0712.3876

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