Individual testing is optimal for nonadaptive group testing in the linear regime

TL;DR

This paper proves that in nonadaptive probabilistic group testing with a constant defect probability, testing items individually is the most efficient method, as no fewer tests can reliably identify defectives.

Contribution

The paper establishes the optimality of individual testing in the linear regime for nonadaptive probabilistic group testing, a previously unresolved question.

Findings

Testing each item individually is optimal in the linear regime.

Fewer than n tests cannot reliably identify defectives.

Error probability remains bounded away from zero with fewer tests.

Abstract

We consider nonadaptive probabilistic group testing in the linear regime, where each of n items is defective independently with probability p in (0,1), and p is a constant independent of n. We show that testing each item individually is optimal, in the sense that with fewer than n tests the error probability is bounded away from zero.