Longest Gapped Repeats and Palindromes

Abstract

A gapped repeat (respectively, palindrome) occurring in a word w is a factor uvu (respectively, \(u^Rvu\)) of w. We show how to compute efficiently, for every position i of the word w, 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 various types of restrictions.