International Symposium on String Processing and Information Retrieval

SPIRE 2015: String Processing and Information Retrieval pp 270-276 | Cite as

Tight Bound for the Number of Distinct Palindromes in a Tree

  • Paweł Gawrychowski
  • Tomasz Kociumaka
  • Wojciech Rytter
  • Tomasz Waleń
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9309)


For an undirected tree with n edges labelled by single letters, we consider its substrings, which are labels of the simple paths between pairs of nodes. We prove that there are \(\mathcal {O}(n^{1.5})\) different palindromic substrings. This solves an open problem of Brlek, Lafrenière and Provençal (DLT 2015), who gave a matching lower-bound construction. Hence, we settle the tight bound of \(\Theta (n^{1.5})\) for the maximum palindromic complexity of trees. For standard strings, i.e., for paths, the palindromic complexity is \(n+1\).


Single Letter Simple Path Standard String Distinct Label Budget Fund 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Paweł Gawrychowski
    • 1
  • Tomasz Kociumaka
    • 1
  • Wojciech Rytter
    • 1
  • Tomasz Waleń
    • 1
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland

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