Bounds for the Number of Tests in Non-Adaptive Randomized Algorithms for Group Testing
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We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model M, let m_ M(n,d) be the minimum number of tests required to detect at most d defectives within n items, with success probability at least 1-δ, for some constant δ. In this paper, we study the measures c_ M(d)=lim_n→∞m_ M(n,d)/ln n c_ M=lim_d→∞c_ M(d)/d. In the literature, the analyses of such models only give upper bounds for c_ M(d) and c_ M, and for some of them, the bounds are not tight. We give new analyses that yield tight bounds for c_ M(d) and c_ M for all the known models M.
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