Optimal adaptive group testing
Abstract
The group testing problem is concerned with identifying a small number $k \sim n^\theta$ for $\theta \in (0,1)$ of infected individuals in a large population of size $n$. At our disposal is a testing procedure that allows us to test groups of individuals. This paper considers twostage designs where the test results of the first stage can inform the design of the second stage. We are interested in the minimum number of tests to recover the set of infected individuals w.h.p. Equipped with a novel algorithm for onestage group testing from [CojaOghlan, Gebhard, HahnKlimroth \& Loick 2019], we propose a polynomialtime twostage algorithm that matches the universal informationtheoretic lower bound of group testing. This result improves on results from [Mézard \& Toninelli 2011] and resolves open problems prominently posed in [Aldridge, Johnson \& Scarlett 2019, Berger \& Levenshtein 2002, Damaschke \& Muhammad 2012].
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.06647
 Bibcode:
 2019arXiv191106647H
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Information Theory;
 68P30;
 05C80;
 60B20