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Small Space Encoding and Recognition of k-Palindromic Prefixes

Authors Gabriel Bathie , Jonas Ellert , Tatiana Starikovskaya

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ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • palindromic length
  • read-only algorithms
  • palindromes

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Abstract

Palindromes are non-empty strings that read the same forward and backward. We study the problem of recognizing so-called k-palindromic strings, which can be represented as the concatenation of exactly k palindromes. [Rubinchik and Shur, MFCS 2020] showed that the problem is solvable in linear space and time. We present a read-only algorithm that recognizes all k-palindromic prefixes of a string T of length n in O(n ⋅ 6^{k²} ⋅ log^k n) time and O(6^{k²} ⋅ log^k n) space. As a corollary, we also obtain a read-only algorithm for computing the palindromic length of T, i.e., the smallest k such that T is k-palindromic, in O(n ⋅ 6^{k²} ⋅ log^⌈k/2⌉ n) time and O(6^{k²} ⋅ log^⌈k/2⌉ n) space.

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Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya. Small Space Encoding and Recognition of k-Palindromic Prefixes. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.9

Author Details

Gabriel Bathie
  • DIENS, École normale supérieure de Paris, PSL Research University, France, LaBRI, Université de Bordeaux, France
Jonas Ellert
  • DIENS, École normale supérieure de Paris, PSL Research University, France
Tatiana Starikovskaya
  • DIENS, École normale supérieure de Paris, PSL Research University, France

Funding

Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya: Partially funded by grant ANR-20-CE48-0001 from the French National Research Agency.

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