Faster Approximate Pattern Matching in Compressed Repetitive Texts

TL;DR

This paper introduces a new data structure for efficiently performing approximate pattern matching on highly repetitive, compressed texts like genomic databases, improving on previous methods by reducing complexity.

Contribution

It presents a simple, space-efficient data structure with improved time complexity for approximate pattern matching in compressed repetitive texts.

Findings

Supports fast substring extraction in compressed texts.

Enables efficient approximate pattern matching with reduced time complexity.

Works with straight-line programs of size proportional to the number of LZ77 phrases.

Abstract

Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the underlying string(s). Bille et al. (2011) recently showed how, given a straight-line program with $r$ rules for a string $s$ of length $n$, we can build an $\Oh{r}$-word data structure that allows us to extract any substring of length $m$ in $\Oh{\log n + m}$ time. They also showed how, given a pattern $p$ of length $m$ and an edit distance (k \leq m), their data structure supports finding all \occ approximate matches to $p$ in $s$ in $\Oh{r (\min (m k, k^4 + m) + \log n) + \occ}$ time. Rytter (2003) and Charikar et al. (2005) showed that $r$ is always at least the number $z$ of phrases in the LZ77 parse of $s$, and gave algorithms for building straight-line programs with $\Oh{z \log n}$ rules. In this paper we give a simple $\Oh{z \log n}$-word data structure that takes the same time for substring extraction but only $\Oh{z \min (m k, k^4 + m) + \occ}$ time for approximate pattern matching.