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arXiv · 1509.00131

Generalising separating families of fixed size

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

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 $Y \subset X$ of exactly $d$ elements by testing, by as few as possible subsets $A$ of $X$, whether $A$ contains an element of $Y$ or not. We are primarily concerned with the model where the family of test sets is specified in advance (non-adaptive) and each test set is of size at most a given $k$. Our main results are asymptotically sharp bounds on the minimum number of tests necessary for fixed $d$ and $k$ and for $n$ tending to infinity.

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Fabrício S. Benevides, Dániel Gerbner, Cory T. Palmer, Dominik K. Vu. 2015-09-01. Generalising separating families of fixed size. https://arxiv.org/abs/1509.00131

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