Lower bounds for oblivious near-neighbor search

Kasper Green Larsen; Tal Malkin; Omri Weinstein; Kevin Yeo

Lower bounds for oblivious near-neighbor search

Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

We prove an Ω(dlg n/(lg lg n)²) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the ddimensional Hamming cube. For the natural setting of d = Θ(lg n), our result implies an Ω(lg ² n) lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for ANN. This is the first super-logarithmic unconditional lower bound for ANN against general (non black-box) data structures. We also show that any oblivious static data structure for decomposable search problems (like ANN) can be obliviously dynamized with O(lg n) overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).

Original language	English
Title of host publication	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Editors	Shuchi Chawla
Publisher	Association for Computing Machinery
Pages	1116-1134
Number of pages	19
ISBN (Electronic)	9781611975994
State	Published - 2020
Externally published	Yes
Event	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States Duration: 5 Jan 2020 → 8 Jan 2020

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2020-January

Conference

Conference	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/Territory	United States
City	Salt Lake City
Period	5/01/20 → 8/01/20

Bibliographical note

Publisher Copyright:
Copyright © 2020 by SIAM

Cite this

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title = "Lower bounds for oblivious near-neighbor search",

abstract = "We prove an Ω(dlg n/(lg lg n)2) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the ddimensional Hamming cube. For the natural setting of d = Θ(lg n), our result implies an Ω(lg 2 n) lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for ANN. This is the first super-logarithmic unconditional lower bound for ANN against general (non black-box) data structures. We also show that any oblivious static data structure for decomposable search problems (like ANN) can be obliviously dynamized with O(lg n) overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).",

author = "Larsen, {Kasper Green} and Tal Malkin and Omri Weinstein and Kevin Yeo",

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year = "2020",

language = "אנגלית",

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booktitle = "31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020",

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Larsen, KG, Malkin, T, Weinstein, O & Yeo, K 2020, Lower bounds for oblivious near-neighbor search. in S Chawla (ed.), 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020-January, Association for Computing Machinery, pp. 1116-1134, 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, United States, 5/01/20.

Lower bounds for oblivious near-neighbor search. / Larsen, Kasper Green; Malkin, Tal; Weinstein, Omri et al.
31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. ed. / Shuchi Chawla. Association for Computing Machinery, 2020. p. 1116-1134 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2020-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Lower bounds for oblivious near-neighbor search

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