Optimal pooling designs with error detection
Optimal pooling designs with error detection
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DOI：
10.1006/jcta.1996.0041
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发表时间：
1996-04-01
影响因子：
1.1
通讯作者：
Torney, DC
中科院分区：
文献类型：
--
作者：
Balding, DJ;Torney, DC
考虑一个对象集合，其中一些对象可能是“坏的”，还有一个最小值，用于确定给定的子集合是否不包含坏对象。非自适应池（或组测试）问题涉及使用并行应用的最少测试数来识别不良对象。“超几何”的情况发生在坏物体数量的上界是先验已知的情况下。在这里，实际的考虑使我们强加了一个额外的要求，即对界的满足进行后验确认。还考虑了在测试结果中可能发生偶然错误的问题的概括。一般问题的最优解等价于一个有限集合的子集的最大集合，它满足了Erdos和同事们所考虑的并集条件。当认为不良对象的数量为1或2时，则导出所需测试次数的下限。在某些情况下，斯坦纳系统被证明是最优解。(C) 1996学术出版社，Inc.
Consider a collection of objects, some of which may be ''bad,'' and a lest which determines whether or not a given subcollection contains no bad objects. The nonadaptive pooling (or group testing) problem involves identifying the bad objects using the least number of tests applied in parallel. The ''hypergeometric'' case occurs when an upper bound on the number of bad objects is known a priori. Here, practical considerations lead us to impose the additional requirement of a posteriori confirmation that the bound is satisfied. A generalization of the problem in which occasional errors in the test outcomes can occur is also considered. Optimal solutions to the general problem are shown to be equivalent to maximum-size collections of subsets of a finite set satisfying a union condition which generalizes that considered by Erdos and co-workers. Lower bounds on the number of tests required are derived when the number of bad objects is believed to be either 1 or 2. Steiner systems are shown to be optimal solutions in some cases. (C) 1996 Academic Press, Inc.