A general framework for sequential batch-testing

Abstract

We provide a generic method that transforms a non-adaptive solution for classic sequential testing problems into a solution for the more general batched setting, while incurring only an additive $\frac{1}{\sqrt{2}}$ fraction loss in the approximation ratio. Combined with previously-known approximation algorithms in the classic setting, we obtain batched algorithms for AND, k-of-n and score-classification functions with approximation ratios 1.707, 2.618 and 6.371 respectively. Our algorithm is very efficient, running in $O\left(n^2\right)$ time for all the aforementioned functions.