Palindromic k-Factorization in Pure Linear Time

Authors Mikhail Rubinchik, Arseny M. Shur

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Mikhail Rubinchik
  • Ural Federal University, Ekaterinburg, Russia
Arseny M. Shur
  • Ural Federal University, Ekaterinburg, Russia

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Mikhail Rubinchik and Arseny M. Shur. Palindromic k-Factorization in Pure Linear Time. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 81:1-81:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Given a string s of length n over a general alphabet and an integer k, the problem is to decide whether s is a concatenation of k nonempty palindromes. Two previously known solutions for this problem work in time O(kn) and O(nlog n) respectively. Here we settle the complexity of this problem in the word-RAM model, presenting an O(n)-time online deciding algorithm. The algorithm simultaneously finds the minimum odd number of factors and the minimum even number of factors in a factorization of a string into nonempty palindromes. We also demonstrate how to get an explicit factorization of s into k palindromes with an O(n)-time offline postprocessing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Combinatorial algorithms
  • stringology
  • palindrome
  • palindromic factorization
  • online algorithm


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