DROPS

Document

DOI: 10.4230/LIPIcs.CCC.2024.11

Linear-Size Boolean Circuits for Multiselection

Authors: Justin Holmgren and Ron Rothblum

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We study the circuit complexity of the multiselection problem: given an input string x ∈ {0,1}ⁿ along with indices i_1,… ,i_q ∈ [n], output (x_{i_1},… ,x_{i_q}). 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.

Cite as

Justin Holmgren and Ron Rothblum. Linear-Size Boolean Circuits for Multiselection. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{holmgren_et_al:LIPIcs.CCC.2024.11,
  author =	{Holmgren, Justin and Rothblum, Ron},
  title =	{{Linear-Size Boolean Circuits for Multiselection}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.11},
  URN =		{urn:nbn:de:0030-drops-204070},
  doi =		{10.4230/LIPIcs.CCC.2024.11},
  annote =	{Keywords: Private Information Retrieval, Batch Selection, Boolean Circuits}
}

Search Results

Documents authored by Rothblum, Ron

Linear-Size Boolean Circuits for Multiselection

Abstract

Cite as

Thanks for your feedback!

Could not send message