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 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 \(O(|T| + \Vert MBP (T)\Vert )\) time, where \(\Vert MBP (T)\Vert \) 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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Notes
- 1.
Block palindromes were firstly introduced in a problem of 2015 British Informatics Olympiad [1], but we did not know the existence at the first version of this paper.
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Goto, K., Tomohiro, I., Bannai, H., Inenaga, S. (2018). Block Palindromes: A New Generalization of Palindromes. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_15
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