Linear-Time Sequence Comparison Using Minimal Absent Words & Applications

TL;DR

This paper introduces a novel linear-time algorithm for comparing sequences based on their minimal absent words, offering an efficient alignment-free method with applications to circular sequences.

Contribution

It presents the first linear-time, linear-space algorithm for sequence comparison using all minimal absent words, advancing alignment-free genomic analysis techniques.

Findings

Algorithm operates in linear time and space

Effective comparison of circular sequences demonstrated

Provides combinatorial insights into minimal absent words

Abstract

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as $q$-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an {\em absent word} of some sequence if it does not occur in the sequence. An absent word is {\em minimal} if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering {\em all} their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.