Paper in proceedings, 2013

Group testing is the problem of identifying up to d defectives in a set 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 no more than d defectives are present. We develop combinatorial tools that are powerful enough to compute many exact t(n,d,s) values. This extends the work of Huang
and Hwang (2001) for s=1 to multistage strategies. The latter are interesting since it is known that asymptotically nearly optimal group testing is possible
already in s=2 stages. Besides other tools we generalize d-disjunct matrices to any candidate hypergraphs, which enables us to express optimal test numbers for s=2 as chromatic numbers of certain conflict graphs. As a proof
of concept we determine almost all test numbers for n up to 10, and t(n,2,2) for some larger n.

nonadaptive

group testing

lower bounds

chromatic number

disjunct matrix

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Vol. 7936 446-457

Basic sciences

Life Science Engineering (2010-2018)

Discrete Mathematics

978-3-642-38767-8