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On Finding Longest Palindromic Subsequences Using Longest Common Subsequences

Authors Gerth Stølting Brodal , Rolf Fagerberg , Casper Moldrup Rysgaard

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Author Details

Gerth Stølting Brodal
  • Aarhus University, Denmark
Rolf Fagerberg
  • University of Southern Denmark, Odense, Denmark
Casper Moldrup Rysgaard
  • Aarhus University, Denmark

Funding

  • Brodal, Gerth Stølting: Independent Research Fund Denmark, grant 9131-00113B.
  • Fagerberg, Rolf: Independent Research Fund Denmark, grant 0135-00420B. EU Horizon Europe, MSC grant 101072930.
  • Rysgaard, Casper Moldrup: Independent Research Fund Denmark, grant 9131-00113B.

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Gerth Stølting Brodal, Rolf Fagerberg, and Casper Moldrup Rysgaard. On Finding Longest Palindromic Subsequences Using Longest Common Subsequences. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.35

Abstract

Two standard textbook problems illustrating dynamic programming are to find the longest common subsequence (LCS) between two strings and to find the longest palindromic subsequence (LPS) of a single string. A popular claim is that the longest palindromic subsequence in a string can be computed as the longest common subsequence between the string and the reversed string. We prove that the correctness of this claim depends on how the longest common subsequence is computed. In particular, we prove that the classical dynamic programming solution by Wagner and Fischer [JACM 1974] for finding an LCS in fact does find an LPS, while a slightly different LCS backtracking strategy makes the algorithm fail to always report a palindrome.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Palindromic subsequence
  • longest common subsequence
  • dynamic programming

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References

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