Identifying defective sets using queries of small size

Fabrício S. Benevides, Dániel Gerbner, Cory T. Palmer, Dominik K. Vu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We examine the following version of a classic combinatorial search problem introduced by Rényi: Given a finite set X of n elements we want to identify an unknown subset Y of X, which is known to have exactly d elements, by means of testing, for as few as possible subsets A of X, whether A intersects Y 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 k. Our main results are nearly tight bounds on the minimum number of tests necessary when d and k are fixed and n is large enough.

Original languageEnglish
Pages (from-to)143-150
Number of pages8
JournalDiscrete Mathematics
Issue number1
StatePublished - Jan 2018


  • Combinatorial search
  • Group testing
  • Separable hypergraphs
  • Union-free hypergraphs


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