J Algebr Comb https://doi.org/10.1007/s10801-018-0828-0 Group testing with geometry of classical groups over ﬁnite ﬁelds 1 2 3 Suogang Gao · Zengti Li · Weili Wu · 4 3 Panos M. Pardalos · Dingzhu Du Received: 14 January 2018 / Accepted: 28 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we give an overview of combinatorial group testing and algebra. Our survey focuses on the constructions with algebraic methods, especially geometry of classical groups over ﬁnite ﬁelds. Keywords Group testing · Pooling design · Classical groups Mathematics Subject Classiﬁcation 05E30 · 05E35 · 33C45 · 33D45 1 Introduction The basic problem of DNA library screening is to determine which clone (a DNA segment) from the library contains which probe from a given collection of probes in an efﬁcient fashion. A clone is said to be positive for a probe if it contains the probe, and negative otherwise. This problem is just an instance of the general group testing problem, in which a large population of items containing a small set of defectives are to be tested to identify the defectives efﬁciently. Suppose there are n clones including at most d positive ones
Journal of Algebraic Combinatorics – Springer Journals
Published: Jun 6, 2018
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