具有错误检测的最优池化设计
Optimal pooling designs with error detection
摘要：
考虑一个对象的集合，其中一些可能是“坏”的，以及一个确定给定子集合是否包含坏对象的测试。非自适应池（或组测试）问题涉及使用并行应用的最少数量的测试来识别坏对象。“超几何”的情况发生时，坏对象的数量的上界是已知的{ \em先验}。在这里，实际的考虑导致我们强加额外的要求{ \em后验}确认的界限得到满足。也被认为是一个泛化的问题，偶尔会发生错误的测试结果。一般问题的最优解被证明是等价于满足工会条件的有限集的子集的最大大小的集合，该条件概括了Erdös \etal \cite{erd}所考虑的。当坏对象的数量被认为是1或2时，导出所需测试数量的下界。Steiner系统在某些情况下是最优解。
英文摘要：
Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive 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 {\em a priori}. Here, practical considerations lead us to impose the additional requirement of {\em 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 Erdös \etal \cite{erd}. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
