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Tracing a single user. (English) Zbl 1105.05068
Denote $$g(n,r)$$ the maximum possible cardinality of a family of subsets of an $$n$$-element underlying set so that given a union of at most $$r$$ members, one can identify at least one of the members. This has a close connection with the so-called group testing problem applied to design DNA chips in molecular biology. The paper shows that $$g(n,r)=2^{\Theta({n \over r})}.$$ The main contribution of the paper is a new lower bound for $$g(n,r)$$.

##### MSC:
 05D05 Extremal set theory 92D20 Protein sequences, DNA sequences
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##### References:
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