Density-based group testing

TL;DR

This paper introduces a generalized group testing model where the test outcome depends on whether the number of defectives exceeds a certain threshold proportion, expanding traditional binary detection methods.

Contribution

It proposes a new density-based group testing framework where test results depend on the density of defectives, providing a novel approach to identify defectives more efficiently.

Findings

New density-based testing model introduced

Analysis of testing strategies under the new model

Potential for reduced testing complexity

Abstract

In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the objects whether they contain at least one defective element. The goal is usually to find all defectives using as few tests as possible. In our model the presence of defective elements in a test set Q can be recognized if and only if their number is large enough compared to the size of Q. More precisely for a test Q the answer is 'yes' if and only if there are at least \alpha |Q| defective elements in Q for some fixed \alpha.