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arXiv · 2008.13209

Tight Bound for the Number of Distinct Palindromes in a Tree

Paweł Gawrychowski·Tomasz Kociumaka·Wojciech Rytter·Tomasz Waleń
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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 $O(n^{1.5})$ different palindromic substrings. This solves an open problem of Brlek, Lafreni\`ere, and Proven\c{c}al (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 $n+1$. We also propose $O(n^{1.5} \log{n})$-time algorithm for reporting all distinct palindromes in an undirected tree with $n$ edges.

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Paweł Gawrychowski, Tomasz Kociumaka, Wojciech Rytter, Tomasz Waleń. 2020-08-30. Tight Bound for the Number of Distinct Palindromes in a Tree. https://arxiv.org/abs/2008.13209

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