Marius Dumitran ; Paweł Gawrychowski ; Florin Manea - Longest Gapped Repeats and Palindromes

dmtcs:1337 - Discrete Mathematics & Theoretical Computer Science, October 13, 2017, Vol. 19 no. 4, FCT '15 -
Longest Gapped Repeats and PalindromesArticle

Authors: Marius Dumitran ; Paweł Gawrychowski ; Florin Manea

    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.

    Volume: Vol. 19 no. 4, FCT '15
    Section: special issue FCT'15
    Published on: October 13, 2017
    Accepted on: October 3, 2017
    Submitted on: October 12, 2016
    Keywords: Computer Science - Data Structures and Algorithms

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