# Rates of adaptive group testing in the linear regime

## TL;DR

This paper analyzes an adaptive group testing algorithm in the linear regime, achieving high information rates for identifying defective items with fewer tests, especially when defectives are less than half of the total.

## Contribution

It provides a detailed analysis of a generalized binary splitting algorithm, demonstrating near-optimal testing rates in the linear regime for both zero-error and small-error scenarios.

## Key findings

- Achieves over 0.9 bits/test for zero-error testing
- Achieves over 0.95 bits/test for small-error testing
- Effective when fewer than half the items are defective

## Abstract

We consider adaptive group testing in the linear regime, where the number of defective items scales linearly with the number of items. We analyse an algorithm based on generalized binary splitting. Provided fewer than half the items are defective, we achieve rates of over 0.9 bits per test for combinatorial zero-error testing, and over 0.95 bits per test for probabilistic small-error testing.