2026-07-22T15:45:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6201 2024-03-06T10:37:48Z ddc:004 open_access

Simple Average-Case Lower Bounds for Approximate Near-Neighbor from Isoperimetric Inequalities Yin, Yitong nearest neighbor search approximate near-neighbor cell-probe model isoperimetric inequality We prove an Omega(d/log(sw/nd)) lower bound for the average-case cell-probe complexity of deterministic or Las Vegas randomized algorithms solving approximate near-neighbor (ANN) problem in ddimensional Hamming space in the cell-probe model with w-bit cells, using a table of size s. This lower bound matches the highest known worst-case cell-probe lower bounds for any static data structure problems. This average-case cell-probe lower bound is proved in a general framework which relates the cell-probe complexity of ANN to isoperimetric inequalities in the underlying metric space. A tighter connection between ANN lower bounds and isoperimetric inequalities is established by a stronger richness lemma proved by cell-sampling techniques. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yitong Yin 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.84 urn:nbn:de:0030-drops-62010 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.84 eng https://creativecommons.org/licenses/by/3.0/legalcode