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arXiv · 1607.00511

On a Hypergraph Approach to Multistage Group Testing Problems

A. G. D'yachkov·I. V. Vorobyev·N. A. Polyanskii·V. Yu. Shchukin
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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.

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A. G. D'yachkov, I. V. Vorobyev, N. A. Polyanskii, V. Yu. Shchukin. 2016-07-02. On a Hypergraph Approach to Multistage Group Testing Problems. https://arxiv.org/abs/1607.00511

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