Faster Approximate String Matching for Short Patterns

TL;DR

This paper introduces a faster algorithm for approximate string matching with short patterns, leveraging tabulation and word-level parallelism to improve time bounds for specific pattern lengths.

Contribution

It presents a novel implementation of the Landau-Vishkin algorithm that significantly accelerates approximate string matching for short patterns on standard hardware.

Findings

Improved time complexity for short pattern matching.

Effective use of tabulation and word-level parallelism.

Enhanced performance when pattern length is subexponential in log n.

Abstract

We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have lengths $m$ and $n$, respectively. On a standard unit-cost word RAM with word size $w \geq \log n$ we present an algorithm using time $$ O(nk \cdot \min(\frac{\log^2 m}{\log n},\frac{\log^2 m\log w}{w}) + n) $$ When $P$ is short, namely, $m = 2^{o(\sqrt{\log n})}$ or $m = 2^{o(\sqrt{w/\log w})}$ this improves the previously best known time bounds for the problem. The result is achieved using a novel implementation of the Landau-Vishkin algorithm based on tabulation and word-level parallelism.