The Power of an Example
Dana Ron, Gilad Tsur · ACM Transactions on Computation Theory · 2016
We study a basic problem of approximating the size of an unknown set S in a known universe U . We consider two versions of the problem. In both versions, the algorithm can specify subsets T ⊆ U . In the first version, which we refer to as the group query or subset query version, the algorithm is told whether T ∩ S is nonempty. In the second version, which we refer to as the subset sampling version, if T ∩ S is nonempty, then the algorithm receives a uniformly selected element from T ∩ S . We study the difference between these two versions in both the case that the algorithm is adaptive and the case in which it is nonadaptive. Our main focus is on a natural family of allowed subsets, which correspond to intervals, as well as variants of this family.