eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-23
84:1
84:13
10.4230/LIPIcs.ICALP.2016.84
article
Simple Average-Case Lower Bounds for Approximate Near-Neighbor from Isoperimetric Inequalities
Yin, Yitong
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol055-icalp2016/LIPIcs.ICALP.2016.84/LIPIcs.ICALP.2016.84.pdf
nearest neighbor search
approximate near-neighbor
cell-probe model
isoperimetric inequality