Finding Approximate Palindromes in Strings Quickly and Simply

TL;DR

This paper introduces two algorithms for efficiently finding long approximate palindromes in strings, such as DNA sequences, with practical performance close to linear time and worst-case guarantees.

Contribution

It presents a simple and a more complex algorithm for approximate palindrome detection, improving efficiency and worst-case complexity guarantees.

Findings

Simple algorithm runs in O(k·n) time in practice

Worst-case complexity is O(n^2), but rarely occurs with biological data

Complex algorithm guarantees O(k·n) worst-case time complexity

Abstract

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the number of ``errors'' allowed in the palindrome. Its worst-case time-complexity is $O(n^2)$ but this does not occur with real biological sequences. A more complex algorithm guarantees $O(k.n)$ worst-case time complexity.