Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations
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xu-haikexu-sm-eecs-2024-thesis.pdf
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Thesis PDF
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1004.77 KB
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80016d782b8cd41d57ff81c755380692
Author(s)
Xu, Haike
Advisor(s)
Indyk, Piotr
Date Issued
May 2024
Publisher
Massachusetts Institute of Technology
Abstract
Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its “slow preprocessing” version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded “intrinsic” dimension. For the other data structure variants studied, including DiskANN with “fast preprocessing”, HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a “reasonable” accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least 0.1n steps on instances of size n before it encounters any of the 5 nearest neighbors of the query.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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