The power of an example: Hidden set size approximation using group queries and conditional sampling

Dana Ron, Gilad Tsur

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number15
JournalACM Transactions on Computation Theory
Volume8
Issue number4
DOIs
StatePublished - Jun 2016

Keywords

  • Approximation
  • Sampling

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