Optimal non-adaptive group testing
arxiv(2019)
摘要
In non-adaptive group testing we aim to identify a small set of $k\sim n^\theta$ infected individuals out of a population size $n$, $0<\theta<1$. We avail ourselves to a test procedure that can test a group of individuals, with the test rendering a positive result iff at least one individual in the group is infected. All tests are conducted in parallel. The aim is to devise a (possibly randomised) test design with as few tests as possible so that the infected individuals can be identified with high probability. We prove that there occurs a sharp information-theoretic/algorithmic phase transition as the number of tests passes an explicit threshold $m_{\inf}$. Hence, if more than $(1+\epsilon)m_{\inf}$ tests are conducted, then there exist a test design and a polynomial time algorithm that identifies the set of infected individuals with high probability. By contrast, identifying the infected individuals is information-theoretically impossible with fewer than $(1-\epsilon)m_{\inf}$ tests. These results resolve problems prominently posed in [Aldridge et al. 2019, Johnson et al. 2018].
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络