On Time-Memory Tradeoffs for Maximal Palindromes with Wildcards and $k$-Mismatches

TL;DR

This paper develops new algorithms for efficiently finding maximal palindromes in texts with wildcards and mismatches, improving time-memory tradeoffs and extending to approximate matching scenarios.

Contribution

It introduces the first linear-space algorithm for maximal palindromes with wildcards and generalizes methods to k-mismatch settings.

Findings

Achieved a continuous time-memory tradeoff for wildcard palindromes.

Presented the first linear-space algorithm for maximal palindromes with wildcards.

Extended algorithms to handle k-mismatches with or without wildcards.

Abstract

This paper addresses the problem of identifying palindromic factors in texts that include wildcards -- special characters that match all others. These symbols challenge many classical algorithms, as numerous combinatorial properties are not satisfied in their presence. We apply existing wildcard-LCE techniques to obtain a continuous time-memory tradeoff, and present the first non-trivial linear-space algorithm for computing all maximal palindromes with wildcards, improving the best known time-memory product in certain parameter ranges. Our main results are algorithms to find and approximate all maximal palindromes in a given text. We also generalize both methods to the $k$-mismatches setting, with or without wildcards.