Derandomization and Group Testing

TL;DR

This paper reviews recent advances in derandomization theory and its applications to combinatorial group testing, highlighting explicit constructions of efficient testing schemes using randomness-conducting functions.

Contribution

It introduces new explicit constructions of group testing schemes leveraging derandomization techniques like extractors and condensers, expanding their applications.

Findings

Construction of error-correcting group testing schemes using extractors

Development of threshold group testing schemes from lossless condensers

Demonstration of near-optimal testing scheme efficiencies

Abstract

The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments related to combinatorial group testing. In its most basic setting, the aim of group testing is to identify a set of "positive" individuals in a population of items by taking groups of items and asking whether there is a positive in each group. In particular, we will discuss explicit constructions of optimal or nearly-optimal group testing schemes using "randomness-conducting" functions. Among such developments are constructions of error-correcting group testing schemes using randomness extractors and condensers, as well as threshold group testing schemes from lossless condensers.