Identifying defective sets using queries of small size |
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Authors: | Fabrício S Benevides Dániel Gerbner Cory T Palmer Dominik K Vu |
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Institution: | 1. Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, CE 60455-760, Brazil;2. Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, P.O.B. 127, Budapest H-1364, Hungary;3. Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA;4. Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA |
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Abstract: | We examine the following version of a classic combinatorial search problem introduced by Rényi: Given a finite set of elements we want to identify an unknown subset of , which is known to have exactly elements, by means of testing, for as few as possible subsets of , whether intersects or not. We are primarily concerned with the non-adaptive model, where the family of test sets is specified in advance, in the case where each test set is of size at most some given natural number . Our main results are nearly tight bounds on the minimum number of tests necessary when and are fixed and is large enough. |
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Keywords: | Group testing Combinatorial search Separable hypergraphs Union-free hypergraphs |
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