Multi-Group Testing for Items with Real-Valued Status under Standard Arithmetic

TL;DR

This paper introduces multi-group testing, a generalization of traditional group testing that tests multi-sets to obtain richer information about items with real-valued statuses, using new $q$-ary additive disjunct matrices.

Contribution

It proposes a novel multi-group testing framework and develops efficient nonadaptive strategies utilizing $q$-ary additive disjunct matrices, extending classical binary disjunct matrices.

Findings

Developed $q$-ary additive $(w,d)$-disjunct matrices

Provided nonadaptive testing strategies for multi-group testing

Enhanced information extraction about items beyond binary defectiveness

Abstract

This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to be tested rather than identify only defectives as was done in conventional group testing. This paper provides efficient nonadaptive strategies for the multi-group testing problem. The major tool is a new structure, $q$-ary additive $(w,d)$-disjunct matrix, which is a generalization of the well-known binary disjunct matrix introduced by Kautz and Singleton in 1964.