We consider threshold group testing – a generalization of group testing, which asks to identify a set of positive individuals in a population, by performing tests on pools of elements. Each test is represented by a subset Q of individuals and its output is yes if Q contains at least one positive element and no otherwise. Threshold group testing is the natural generalization, introduced by P. Damaschke in 2005, arising when we are given a threshold $t>0$ and the answer to a test Q is yes if Q contains at least t positives and no otherwise. We give upper and lower bounds for this general problem, showing a complexity separation with the classical group testing. Next, we introduce a further generalization in which the goal is minimizing not only the number of tests, but also the number of thresholds which is related to the accuracy of the tests.

我们认为门槛组测试-的推广组的测试，它要求以确定一套积极的人在人群中，通过对元素池进行测试。每个测试是通过一个子集表示Q个体，并且其输出是是如果Q包含至少一个正元件和没有其它。阈值组测试是P. Damaschke在2005年提出的自然概括，它是在给定阈值后产生的$Ť>0$而答案在测试Q是肯定的，如果Q包含至少含有t阳性，没有其他。我们给出了这个一般问题的上限和下限，显示了与经典组测试的复杂性分离。接下来，我们引入进一步的概括，其目标是不仅使测试次数最少，而且使与测试准确性相关的阈值数量最少。