Tracing a single user

Authors:
Noga Alon;Vera Asodi
Affiliations:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel;School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
Venue:
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Year:
2006

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Abstract

Let g (n, r) be the maximum possible cardinality of a family F of subsets of {1, 2,...,n} so that given a union of at most r members of F, one can identify at least one of these members. The study of this function is motivated by questions in molecular biology. We show that g(n, r) = 2Θ(n/r), thus solving a problem of Csürös and Ruszinkó.