Year: 2016
Type: conference-paper
Abstract: Group testing is a well known search problem that consists in detecting up to s, s ≪ t, defective elements of the set [t] = {1, . . . , 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 defective elements. For the case s = 2 and t → ∞, we design an explicit construction, which makes use of 2 log2t(1 + o(1)) tests in the worst case and consists of 4 stages. For the general case of fixed s > 2 and t → ∞, we provide an explicit construction, which uses (2s - 1) log2t(1+o(1)) tests and consists of 2s - 1 rounds.
Authors: A. G. D'yachkov, I.V. Vorobyev, N.A. Polyanskii, V.Yu. Shchukin
Institution: Lomonosov Moscow State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2271689317