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

2026-04-22

AI Summary

This study addresses the problem of efficiently identifying the longest palindromic substring in strings containing wildcards, where each wildcard can match any character and thereby disrupts the symmetry exploited by classical palindrome-finding algorithms. To overcome this challenge, we present the first non-trivial algorithm that operates within linear space, leveraging a novel wildcard-based longest common extension (wildcard-LCE) technique. Our approach establishes a continuous trade-off between time and memory usage, achieving substantial improvements in the time–memory product across a range of parameter settings. Furthermore, the method generalizes effectively to the more challenging setting allowing up to k mismatches, yielding both theoretical advances and practical performance gains.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Life-Long and Continual Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• maximal palindromes
• wildcards
• k-mismatches
• time-memory tradeoffs

Innovation

• wildcard palindromes
• time-memory tradeoff
• linear-space algorithm
• k-mismatches
• maximal palindromes