Strict group testing and the set basis problem
Artikel i vetenskaplig tidskrift, 2014

Group testing is the problem to identify up to d defectives out of n elements, by testing subsets for the presence of defectives. Let t(n,d,s) be the optimal number of tests needed by an s-stage strategy in the strict group testing model where the searcher must also verify that at most d defectives are present. We start building a combinatorial theory of strict group testing. We compute many exact t(n,d,s) values, thereby extending known results for s=1 to multistage strategies. These are interesting since asymptotically nearly optimal group testing is possible already in s=2 stages. Besides other combinatorial tools we generalize d-disjunct matrices to any candidate hypergraphs, and we reveal connections to the set basis problem and communication complexity. As a proof of concept we apply our tools to determine almost all test numbers for n<10 and some further t(n,2,2) values. We also show t(n,2,2)<2.44*log n+o(log n).

group testing

d-disjunct matrix

graph coloring

set basis

hypergraph

Författare

Peter Damaschke

Chalmers, Data- och informationsteknik, Datavetenskap

Muhammad Azam Sheikh

Chalmers, Data- och informationsteknik, Datavetenskap

Gabor Wiener

Budapesti Muszaki es Gazdasagtudomanyi Egyetem

Journal of Combinatorial Theory - Series A

0097-3165 (ISSN)

Vol. 126 70-91

Fundament

Grundläggande vetenskaper

Ämneskategorier

Diskret matematik

DOI

10.1016/j.jcta.2014.04.005