On a Hypergraph Approach to Multistage Group Testing Problems
Abstract
Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find all defective elements by using the minimal possible number of tests. In this paper we consider multistage group testing. We propose a general idea how to use a hypergraph approach to searching defects. For the case $s=2$, we design an explicit construction, which makes use of $2\log_2t(1+o(1))$ tests in the worst case and consists of $4$ stages.
 Publication:

arXiv eprints
 Pub Date:
 July 2016
 DOI:
 10.48550/arXiv.1607.00511
 arXiv:
 arXiv:1607.00511
 Bibcode:
 2016arXiv160700511D
 Keywords:

 Computer Science  Information Theory
 EPrint:
 ACCT 2016, 6 pages