 
Summary: Tracing a single user
Noga Alon
Vera Asodi
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) = 2( n
r )
,
thus solving a problem of Csur¨os and Ruszink´o.
1 Introduction
Let [n] = {1, 2, . . . , n}, and let F 2[n] be a family of subsets of [n]. F is called rsuperimposed if
for all A1, . . . , Ak, B1, . . . , Bl F with k, l r and {A1, . . . , Ak} = {B1, . . . , Bl},
k
i=1
Ai =
l
i=1
Bi.
This means that, given the union of up to r sets from an rsuperimposed family, one can identify all
