We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We develop an adaptive group testing algorithm that uses the proposed set formation method recursively. We prove novel upper bounds on the number of tests for the proposed algorithm. Via numerical results, we show that our algorithm outperforms the state of the art, and performs close to the entropy lower bound.
翻译:我们认为,在个人独立存在缺陷但概率不完全相同的情况下,存在一个零性概率群体测试问题。我们建议采用贪婪的组合组装法来构建一组要一起测试的个人。我们开发了适应性组装测试算法,同时使用拟议组装法进行递归。我们证明,对拟议算法的测试数量来说,我们具有新的上限。通过数字结果,我们显示,我们的算法优于最新水平,并运行接近低约束的导体。