Linear-Size Boolean Circuits for Multiselection

Justin Holmgren, Ron Rothblum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the circuit complexity of the multiselection problem: given an input string x ∈ {0, 1}n along with indices i1, . . ., iq ∈ [n], output (xi1, . . ., xiq). A trivial lower bound for the circuit size is the input length n + q · log(n), but the straightforward construction has size Θ(q · n). Our main result is an O(n + q · log3(n))-size and O(log(n + q))-depth circuit for multiselection. In particular, for any q ≤ n/log3(n) the circuit has linear size and logarithmic depth. Prior to our work no linear-size circuit for multiselection was known for any q = ω(1) and regardless of depth.

Original languageEnglish
Title of host publication39th Computational Complexity Conference, CCC 2024
EditorsRahul Santhanam
ISBN (Electronic)9783959773317
DOIs
StatePublished - Jul 2024
Event39th Computational Complexity Conference, CCC 2024 - Ann Arbor, United States
Duration: 22 Jul 202425 Jul 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume300

Conference

Conference39th Computational Complexity Conference, CCC 2024
Country/TerritoryUnited States
CityAnn Arbor
Period22/07/2425/07/24

Keywords

  • Batch Selection
  • Boolean Circuits
  • Private Information Retrieval

All Science Journal Classification (ASJC) codes

  • Software

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