Cited by 1,067Advanced Image and Video Retrieval TechniquesAlgorithms and Data CompressionComplexity and Algorithms in Graphs

Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

Andoni, Alexandr, Indyk, Piotr·2006·2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

Abstract

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn1c2/+o(1)) and space O(dn + n1+1c2/+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in (R. Motwani et al., 2006). We also obtain a space-efficient version of the algorithm, which uses dn+n logO(1)n space, with a query time of dnO(1/c2). Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech lattice

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Crossref · 10.1109/focs.2006.49

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Authors
Andoni, A., & Indyk, P.
Affiliations
Massachusetts Institute of Technology (US)
Venue
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
Publisher
IEEE
Published
2006
Pages
459-468
ISSN
0272-5428 (ISSN-L)
OpenAlex
W2145065594
Cited by
1,067
References
47
Citations by year
2026: 3 · 2025: 21 · 2024: 21 · 2023: 22 · 2022: 44 · 2021: 77 · 2020: 87 · 2019: 82 · 2018: 108 · 2017: 95 · 2016: 85 · 2015: 99 · 2014: 90 · 2013: 49 · 2012: 50
FWCI
16.14
Type
conference paper
Language
en
Open access
closed
Locations
Annual Symposium on Foundations of Computer Science (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image and Video Retrieval Techniques
  • Physical Sciences › Computer Science › Artificial Intelligence › Algorithms and Data Compression
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
Keywords
approximate nearest neighbor search, hash algorithms, high-dimensional Euclidean space, query response time, space complexity, lower bounds, space-efficient data structures, bounded distance decoding, Leech lattice, lattice-based algorithms

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