# A New Algorithm for Two-Stage Group Testing

## TL;DR

This paper introduces a new two-stage group testing algorithm using hypergraph methods, achieving near-optimal test efficiency for large sample sets and addressing partial defect detection.

## Contribution

The paper presents a novel hypergraph-based algorithm for two-stage group testing that improves known bounds and achieves near-optimal performance for large sample sizes.

## Key findings

- Achieves the information-theoretic lower bound for s=2 as t→∞.
- Improves known results for fixed s and large t.
- Addresses the problem of identifying m out of s defectives.

## Abstract

Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests in the worst case. In this work, two-stage group testing is considered. Using the hypergraph approach we design a new search algorithm, which allows improving the known results for fixed $s$ and $t\to\infty$. For the case $s=2$ this algorithm achieves information-theoretic lower bound $2\log_2t(1+o(1))$ on the number of tests in the worst case. Also, the problem of finding $m$ out of $s$ defectives is considered.