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)

Abstract

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 \(n+1\).

Keywords

Single Letter Simple Path Standard String Distinct Label Budget Fund 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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