License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.84
URN: urn:nbn:de:0030-drops-62010
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6201/
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Yin, Yitong

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

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LIPIcs-ICALP-2016-84.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{yin:LIPIcs:2016:6201,
  author =	{Yitong Yin},
  title =	{{Simple Average-Case Lower Bounds for Approximate Near-Neighbor from Isoperimetric Inequalities}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{84:1--84:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6201},
  URN =		{urn:nbn:de:0030-drops-62010},
  doi =		{10.4230/LIPIcs.ICALP.2016.84},
  annote =	{Keywords: nearest neighbor search, approximate near-neighbor, cell-probe model, isoperimetric inequality}
}

Keywords: nearest neighbor search, approximate near-neighbor, cell-probe model, isoperimetric inequality
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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