Faster deterministic and Las vegas algorithms for offline approximate nearest neighbors in high dimensions
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1.9781611975994.39.pdf
Description
Published version
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615.83 KB
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Adobe PDF
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0fe24e8b3f5284f848b22dc408655f59
Author(s)
Alman, Joshua
Williams, R Ryan
Date Issued
January 2020
Journal
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Association for Computing Machinery
Citation
Alman, Josh et al. “Faster deterministic and Las vegas algorithms for offline approximate nearest neighbors in high dimensions.” Paper in the Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, Utah, January 5 - 8, 2020, Association for Computing Machinery: 637-649 © 2020 The Author(s)
Version
Final published version
Abstract
We present a deterministic, truly subquadratic algorithm for offline (1 + ε)-approximate nearest or farthest neighbor search (in particular, the closest pair or diameter problem) in Hamming space in any dimension d ≤ nδ, for a sufficiently small constant δ > 0. The running time of the algorithm is roughly n2−ε1/2+O(δ) for nearest neighbors, or n2−Ω(√ε/log(1/ε)) for farthest. The algorithm follows from a simple combination of expander walks, Chebyshev polynomials, and rectangular matrix multiplication. We also show how to eliminate errors in the previous Monte Carlo randomized algorithm of Alman, Chan, and Williams [FOCS'16] for offline approximate nearest or farthest neighbors, and obtain a Las Vegas randomized algorithm with expected running time n2−Ω(ε1/3/log(1/ε)) . Finally, we note a simplification of Alman, Chan, and Williams' method and obtain a slightly improved Monte Carlo randomized algorithm with running time n2−Ω(ε1/3/log2/3(1/ε)) . As one application, we obtain improved deterministic and randomized (1+ε)-approximation algorithms for MAX-SAT.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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DOI of Published Version
https://doi.org/10.1137/1.9781611975994.39
