Efficient pattern matching in degenerate strings with the Burrows-Wheeler transform

TL;DR

This paper introduces a new hybrid pattern-matching method based on the Burrows-Wheeler transform for efficiently searching degenerate strings, applicable to both regular and indeterminate sequences, with practical performance benefits.

Contribution

It presents a novel BWT-based approach for degenerate string pattern matching, including a specialized method for conservative strings with bounded non-solid letters.

Findings

Method runs in O(mn) time for general degenerate strings.

For conservative strings, search complexity reduces to O(qm^2).

Experimental results demonstrate practical efficiency.

Abstract

A degenerate or indeterminate string on an alphabet $\Sigma$ is a sequence of non-empty subsets of $\Sigma$. Given a degenerate string $t$ of length $n$, we present a new method based on the Burrows--Wheeler transform for searching for a degenerate pattern of length $m$ in $t$ running in $O(mn)$ time on a constant size alphabet $\Sigma$. Furthermore, it is a hybrid pattern-matching technique that works on both regular and degenerate strings. A degenerate string is said to be conservative if its number of non-solid letters is upper-bounded by a fixed positive constant $q$; in this case we show that the search complexity time is $O(qm^2)$. Experimental results show that our method performs well in practice.