Longest Gapped Repeats and Palindromes - Dumitran, Marius; Gawrychowski, Paweł; Manea, Florin (arXiv.org, 2017)
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.