Finding approximate palindromes in strings

TL;DR

This paper introduces a new concept of approximate palindromes in strings, along with an efficient algorithm to find all maximal instances with up to k errors, supported by practical experiments and analysis.

Contribution

It presents a novel definition of approximate palindromes and an algorithm with $O(k^2 n)$ complexity to find all maximal instances, including implementation improvements.

Findings

Algorithm runs in $O(k^2 n)$ time for fixed alphabet.

Implementation improvements enhance practical performance.

Experimental and average-case analysis validate efficiency.

Abstract

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of approximate pattern matching, and the algorithm we give, for a string of size $n$ on a fixed alphabet, runs in $O(k^2 n)$ time. We also discuss two implementation-related improvements to the algorithm, and demonstrate their efficacy in practice by means of both experiments and an average-case analysis.