He Yichao, Tian Haiyan, Zhang Xinlu, Wang Zhiwei, Gao Suogang
Information Engineering School, Shijiazhuang University of Economics, Shijiazhuang, China.
J Comput Biol. 2012 Jul;19(7):903-10. doi: 10.1089/cmb.2011.0229. Epub 2012 Mar 8.
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).
如果一个分组测试包含至少(u)个（至多(l)个）阳性样本，则该测试给出阳性（阴性）结果；如果阳性样本的数量在阈值(l)和(u)之间，则给出任意结果。Damaschke提出的这个问题称为阈值分组测试。它是经典分组测试的推广。Chen和Fu将这个问题扩展到了容错版本，并首次提出了高效的非自适应算法。在本文中，我们将阈值分组测试扩展到(k)抑制器模型，在该模型中，如果一个测试包含至少(u)个阳性样本且至多(k - 1)个抑制器，则该测试给出阳性结果。通过使用((d + k - l, u; 2e + 1])-析取矩阵，我们为具有(k)抑制器且至多有(e)个错误结果的阈值分组测试模型提供了非自适应算法。对于固定参数((d, u, l, k, e))，解码复杂度为(O(n(u + k)\log n))。
