2026-07-23T20:08:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20407 2024-07-15T12:26:45Z ddc:004 open_access

Linear-Size Boolean Circuits for Multiselection Holmgren, Justin Rothblum, Ron Private Information Retrieval Batch Selection Boolean Circuits 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Justin Holmgren and Ron Rothblum 2024 Is Part Of LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2024.11 urn:nbn:de:0030-drops-204070 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.11 eng https://creativecommons.org/licenses/by/4.0/legalcode