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Locality-Sensitive Bucketing Functions for the Edit Distance

Authors Ke Chen , Mingfu Shao

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Author Details

Ke Chen
  • Department of Computer Science and Engineering, School of Electronic Engineering and Computer Science, The Pennsylvania State University, University Park, PA, United States
Mingfu Shao
  • Department of Computer Science and Engineering, School of Electronic Engineering and Computer Science, The Pennsylvania State University, University Park, PA, United States
  • Huck Institutes of the Life Sciences, The Pennsylvania State University, University Park, PA, United States

Funding

This work is supported by the US National Science Foundation (DBI-2019797) and the US National Institutes of Health (R01HG011065).

Cite AsGet BibTex

Ke Chen and Mingfu Shao. Locality-Sensitive Bucketing Functions for the Edit Distance. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.WABI.2022.22

Abstract

Many bioinformatics applications involve bucketing a set of sequences where each sequence is allowed to be assigned into multiple buckets. To achieve both high sensitivity and precision, bucketing methods are desired to assign similar sequences into the same bucket while assigning dissimilar sequences into distinct buckets. Existing k-mer-based bucketing methods have been efficient in processing sequencing data with low error rate, but encounter much reduced sensitivity on data with high error rate. Locality-sensitive hashing (LSH) schemes are able to mitigate this issue through tolerating the edits in similar sequences, but state-of-the-art methods still have large gaps. Here we generalize the LSH function by allowing it to hash one sequence into multiple buckets. Formally, a bucketing function, which maps a sequence (of fixed length) into a subset of buckets, is defined to be (d₁, d₂)-sensitive if any two sequences within an edit distance of d₁ are mapped into at least one shared bucket, and any two sequences with distance at least d₂ are mapped into disjoint subsets of buckets. We construct locality-sensitive bucketing (LSB) functions with a variety of values of (d₁,d₂) and analyze their efficiency with respect to the total number of buckets needed as well as the number of buckets that a specific sequence is mapped to. We also prove lower bounds of these two parameters in different settings and show that some of our constructed LSB functions are optimal. These results provide theoretical foundations for their practical use in analyzing sequences with high error rate while also providing insights for the hardness of designing ungapped LSH functions.

Subject Classification

ACM Subject Classification
  • Applied computing → Bioinformatics
  • Applied computing → Computational biology
Keywords
  • Locality-sensitive hashing
  • locality-sensitive bucketing
  • long reads
  • embedding

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Supplementary Materials

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