Group Testing with Non-identical Infection Probabilities

TL;DR

This paper introduces an adaptive group testing algorithm for individuals with different infection probabilities, using a greedy set formation method to improve efficiency and approach theoretical lower bounds.

Contribution

It presents a novel recursive adaptive testing algorithm with a greedy set formation approach tailored for non-identical infection probabilities.

Findings

Outperforms existing algorithms in numerical tests

Achieves test counts close to entropy lower bounds

Provides new upper bounds on tests needed

Abstract

We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We develop an adaptive group testing algorithm that uses the proposed set formation method recursively. We prove novel upper bounds on the number of tests for the proposed algorithm. Via numerical results, we show that our algorithm outperforms the state of the art, and performs close to the entropy lower bound.