On a Hypergraph Approach to Multistage Group Testing Problems

TL;DR

This paper introduces a hypergraph-based method for multistage group testing, providing explicit constructions that efficiently identify defective elements with minimal tests and stages.

Contribution

It presents a novel hypergraph approach to multistage group testing and offers an explicit construction for the case s=2 with optimized test count and stages.

Findings

Uses 2 log2 t (1+o(1)) tests for s=2

Constructs a 4-stage testing procedure

Efficiently identifies up to 2 defective elements

Abstract

Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests. In this paper we consider multistage group testing. We propose a general idea how to use a hypergraph approach to searching defects. For the case $s=2$, we design an explicit construction, which makes use of $2\log_2t(1+o(1))$ tests in the worst case and consists of $4$ stages.