Geodesic
Longest Gapped Repeats and Palindromes
Discrete mathematics & theoretical computer science, FCT '15, Tome 19 (2017-2018) no. 4.

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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. 
@article{DMTCS_2017_19_4_a0,
     author = {Dumitran, Marius and Gawrychowski, Pawe{\l} and Manea, Florin},
     title = {Longest {Gapped} {Repeats} and {Palindromes}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-4-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-4-4/}
}
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Dumitran, Marius; Gawrychowski, Paweł; Manea, Florin. Longest Gapped Repeats and Palindromes. Discrete mathematics & theoretical computer science, FCT '15, Tome 19 (2017-2018) no. 4. doi : 10.23638/DMTCS-19-4-4. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-4-4/

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