Subsets and supermajorities: Optimal hashing-based set similarity search

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  • Thomas D. Ahle
  • Jakob B.T. Knudsen

We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric Approximate Set Similarity Search problem, including approximate versions of Subset Search, Maximum Inner Product Search (MIPS), Jaccard Similarity Search, and Partial Match. Our algorithm can be seen as a natural generalization of previous work on Set as well as Euclidean Similarity Search, but conceptually it differs by optimally exploiting the information present in the sets as well as their complements, and doing so asymmetrically between queries and stored sets. Doing so we improve upon the best previous work: MinHash [J. Discrete Algorithms 1998], SimHash [STOC 2002], Spherical LSF [SODA 2016, 2017], and Chosen Path [STOC 2017] by as much as a factor n{0.14} in both time and space; or in the near-constant time regime, in space, by an arbitrarily large polynomial factor. Turning the geometric concept, based on Boolean supermajority functions, into a practical algorithm requires ideas from branching random walks on mathbb{Z}{2}, for which we give the first non-asymptotic near tight analysis. Our lower bounds follow from new hypercontractive arguments, which can be seen as characterizing the exact family of similarity search problems for which supermajorities are optimal. The optimality holds for among all hashing based data structures in the random setting, and by reductions, for 1 cell and 2 cell probe data structures.

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
Publication date2020
Article number9317929
ISBN (Electronic)9781728196213
Publication statusPublished - 2020
Event61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States
Duration: 16 Nov 202019 Nov 2020


Conference61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
LandUnited States
ByVirtual, Durham
SponsorIEEE Computer Society Technical Committee on Mathematical Foundations of Computing
SeriesProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

    Research areas

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ID: 258712597