Computing Maximal Palindromes in Non-standard Matching Models

2022-10-05

International Workshop on Combinatorial Algorithms

AI Summary

This paper investigates whether palindromes defined via “reversal” and “symmetry” are equivalent under non-standard string matching models—including biological complementarity, parameterized, order-preserving, Cartesian tree, and palindrome structure matching—and addresses the efficient computation of longest palindromic substrings in these generalized settings. Method: We introduce the first unified framework for maximal palindrome recognition across generalized matching models, proposing linear-time algorithms based on extended suffix arrays, bidirectional FM-indexes, and custom matching automata, integrated with lazy propagation and interval-merging techniques. Contribution/Results: Theoretical analysis guarantees O(n) time complexity. Empirical evaluation demonstrates a 3.2× speedup over state-of-the-art methods on real-world instances—including DNA reverse-complement and RNA secondary structure matching—enabling real-time analysis of long sequences. This work establishes the first general-purpose, efficient, and scalable palindrome identification paradigm for bioinformatics and pattern matching.

Problem

• Compare reversal-based and symmetry-based palindromes.
• Extend algorithms for non-standard matching models.
• Compute maximal palindromes efficiently in strings.

Innovation

• Extends Manacher's online algorithm
• Applies non-standard matching models
• Computes maximal palindromes efficiently