Approximate Similarity Search Under Edit Distance Using Locality-sensitive Hashing

Mccauley Samuel. Arxiv 2019

[Paper]    
ARXIV Independent

Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread database applications. The goal of the problem is to preprocess \(n\) strings of length \(d\), to quickly answer queries \(q\) of the form: if there is a database string within edit distance \(r\) of \(q\), return a database string within edit distance \(cr\) of \(q\). Previous approaches to this problem either rely on very large (superconstant) approximation ratios \(c\), or very small search radii \(r\). Outside of a narrow parameter range, these solutions are not competitive with trivially searching through all \(n\) strings. In this work give a simple and easy-to-implement hash function that can quickly answer queries for a wide range of parameters. Specifically, our strategy can answer queries in time \(\tilde{O}(d3^rn^{1/c})\). The best known practical results require \(c \gg r\) to achieve any correctness guarantee; meanwhile, the best known theoretical results are very involved and difficult to implement, and require query time at least \(24^r\). Our results significantly broaden the range of parameters for which we can achieve nontrivial bounds, while retaining the practicality of a locality-sensitive hash function. We also show how to apply our ideas to the closely-related Approximate Nearest Neighbor problem for edit distance, obtaining similar time bounds.

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