Nonadaptive Algorithms for Threshold Group Testing with Inhibitors and Error-Tolerance

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A group test gives a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome if the number of positive items is between thresholds l and u. This problem introduced by Damaschke is called threshold group testing. It is a generalization of classical group testing. Chen and Fu extended this problem to the error-tolerant version and first proposed efficient nonadaptive algorithms. In this article, we extend threshold group testing to the k-inhibitors model in which a test has a positive outcome if it contains at least u positives and at most k-1 inhibitors. By using (d + k - l, u; 2e + 1]-disjunct matrix we provide nonadaptive algorithms for the threshold group testing model with k-inhibitors and at most e-erroneous outcomes. The decoding complexity is O(n(u+k) log n) for fixed parameters (d, u, l, k, e).