An optimization problem in statistical databases

Abstract

Let D = {a1, . . ,an} be a set of real numbers, and let S ⊂ {1, . , n}. For an interval I ⊂ {1, . . . , n} we set SUM (I) = ∑i∈I ai. In this paper we solve the following problem which has been asked in connection with security of statistical databases: Find a largest family B of subintervals of {1, . . . , n} so that knowing the value of SUM (I) for all I ∈ B does not enable one to calculate any element ai ∈ D, where i ∈ S.