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In the classical non-adaptive group testing setup, pools of items are testedtogether, and the main goal of a recovery algorithm is to identify the"complete defective set" given the outcomes of different group tests. Incontrast, the main goal of a "non-defective subset recovery" algorithm is toidentify a "subset" of non-defective items given the test outcomes. In thispaper, we present a suite of computationally efficient and analyticallytractable non-defective subset recovery algorithms. By analyzing theprobability of error of the algorithms, we obtain bounds on the number of testsrequired for non-defective subset recovery with arbitrarily small probabilityof error. Our analysis accounts for the impact of both the additive noise(false positives) and dilution noise (false negatives). By comparing with theinformation theoretic lower bounds, we show that the upper bounds on the numberof tests are order-wise tight up to a $\log^2K$ factor, where $K$ is the numberof defective items. We also provide simulation results that compare therelative performance of the different algorithms and provide further insightsinto their practical utility. The proposed algorithms significantly outperformthe straightforward approaches of testing items one-by-one, and of firstidentifying the defective set and then choosing the non-defective items fromthe complement set, in terms of the number of measurements required to ensure agiven success rate.

Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population