Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes

TL;DR

This paper introduces efficient non-adaptive and two-stage combinatorial group testing algorithms that minimize the number of tests needed to identify defective items in large sets, matching theoretical lower bounds in some cases.

Contribution

The paper presents practically efficient algorithms for combinatorial group testing, including a two-stage method that achieves the information theoretic lower bound for the number of tests.

Findings

Two-stage algorithm matches the information theoretic lower bound.

Algorithms significantly reduce the number of tests needed.

Applicable to real-world problem sizes.

Abstract

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.