Optimal Randomized Group Testing Algorithm to Determine the Number of Defectives

TL;DR

This paper presents an optimized adaptive group testing algorithm that accurately determines the number of defectives with minimal tests, establishing near-optimal efficiency through theoretical bounds.

Contribution

It introduces a new adaptive testing algorithm and proves a lower bound, demonstrating the algorithm's near-optimality in test efficiency.

Findings

The proposed algorithm minimizes the number of tests needed.

Theoretical lower bounds confirm the near-optimality of the algorithm.

The method improves upon previous group testing strategies.

Abstract

We study the problem of determining exactly the number of defective items in an adaptive Group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our algorithm is optimal up to small additive terms.