TY - JOUR

T1 - The power of an example

T2 - Hidden set size approximation using group queries and conditional sampling

AU - Ron, Dana

AU - Tsur, Gilad

N1 - Publisher Copyright:
© 2016 ACM.

PY - 2016/6

Y1 - 2016/6

N2 - 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.

AB - 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.

KW - Approximation

KW - Sampling

UR - http://www.scopus.com/inward/record.url?scp=84976449592&partnerID=8YFLogxK

U2 - 10.1145/2930657

DO - 10.1145/2930657

M3 - מאמר

AN - SCOPUS:84976449592

VL - 8

JO - ACM Transactions on Computation Theory

JF - ACM Transactions on Computation Theory

SN - 1942-3454

IS - 4

M1 - 15

ER -