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arXiv · 1806.00198

Block Palindromes: A New Generalization of Palindromes

Keisuke Goto·Tomohiro I·Hideo Bannai·Shunsuke Inenaga
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Abstract

We study a new generalization of palindromes and gapped palindromes called block palindromes. A block palindrome is a string that becomes a palindrome when identical substrings are replaced with a distinct character. We investigate several properties of block palindromes and in particular, study substrings of a string which are block palindromes. In so doing, we introduce the notion of a \emph{maximal block palindrome}, which leads to a compact representation of all block palindromes that occur in a string. We also propose an algorithm which enumerates all maximal block palindromes that appear in a given string $T$ in $O(|T| + \|\mathit{MBP}(T)\|)$ time, where $\|\mathit{MBP}(T)\|$ is the output size, which is optimal unless all the maximal block palindromes can be represented in a more compact way.

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Keisuke Goto, Tomohiro I, Hideo Bannai, Shunsuke Inenaga. 2018-06-01. Block Palindromes: A New Generalization of Palindromes. https://arxiv.org/abs/1806.00198

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