@inproceedings{fcd9dab8ecbf4739b27f74ef618370f2,
title = "Linear-Size Boolean Circuits for Multiselection",
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.",
keywords = "Batch Selection, Boolean Circuits, Private Information Retrieval",
author = "Justin Holmgren and Ron Rothblum",
note = "Publisher Copyright: {\textcopyright} Justin Holmgren and Ron Rothblum.; 39th Computational Complexity Conference, CCC 2024 ; Conference date: 22-07-2024 Through 25-07-2024",
year = "2024",
month = jul,
doi = "https://doi.org/10.4230/LIPIcs.CCC.2024.11",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Rahul Santhanam",
booktitle = "39th Computational Complexity Conference, CCC 2024",
}