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Simple Average-Case Lower Bounds for Approximate Near-Neighbor from Isoperimetric Inequalities

Author Yitong Yin



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Yitong Yin

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Yitong Yin. Simple Average-Case Lower Bounds for Approximate Near-Neighbor from Isoperimetric Inequalities. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 84:1-84:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ICALP.2016.84

Abstract

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.
Keywords
  • nearest neighbor search
  • approximate near-neighbor
  • cell-probe model
  • isoperimetric inequality

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