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

dmtcs:3988 - Discrete Mathematics & Theoretical Computer Science, October 13, 2017, vol 19 no. 4, FCT '15
Longest Gapped Repeats and Palindromes

Authors: Dumitran, Marius and Gawrychowski, Paweł and Manea, Florin

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.

Source : oai:arXiv.org:1511.07180
Volume: vol 19 no. 4, FCT '15
Section: special issue FCT'15
Published on: October 13, 2017
Submitted on: October 12, 2016
Keywords: Computer Science - Data Structures and Algorithms