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arXiv · 1511.07180

Longest Gapped Repeats and Palindromes

Marius Dumitran·Paweł Gawrychowski·Florin Manea
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Abstract

A gapped repeat (respectively, palindrome) occurring in a word $w$ is a factor $uvu$ (respectively, $u^Rvu$) of $w$. In such a repeat (palindrome) $u$ is called the arm of the repeat (respectively, palindrome), while $v$ is called the gap. We show how to compute efficiently, for every position $i$ of the word $w$, the longest gapped repeat and palindrome occurring at that position, provided that the length of the gap is subject to various types of restrictions. That is, that for each position $i$ we compute the longest prefix $u$ of $w[i..n]$ such that $uv$ (respectively, $u^Rv$) is a suffix of $w[1..i-1]$ (defining thus a gapped repeat $uvu$ -- respectively, palindrome $u^Rvu$), and the length of $v$ is subject to the aforementioned restrictions.

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Marius Dumitran, Paweł Gawrychowski, Florin Manea. 2015-11-23. Longest Gapped Repeats and Palindromes. https://doi.org/10.23638/dmtcs-19-4-4

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