Abstract
Group testing is the problem of identifying up to d defectives in a set of n elements by testing subsets for the presence of defectives. Let t(n,d,s) be the optimal number of tests needed by an s-stage strategy in the strict group testing model where the searcher must also verify that no more than d defectives are present. We develop combinatorial tools that are powerful enough to compute many exact t(n,d,s) values. This extends the work of Huang and Hwang (2001) for s = 1 to multistage strategies. The latter are interesting since it is known that asymptotically nearly optimal group testing is possible already in s = 2 stages. Besides other tools we generalize d-disjunct matrices to any candidate hypergraphs, which enables us to express optimal test numbers for s = 2 as chromatic numbers of certain conflict graphs. As a proof of concept we determine almost all test numbers for n ≤ 10, and t(n,2,2) for some larger n.
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Damaschke, P., Muhammad, A.S. (2013). A Toolbox for Provably Optimal Multistage Strict Group Testing Strategies. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_40
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DOI: https://doi.org/10.1007/978-3-642-38768-5_40
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