OMPPM: Online multiple palindrome pattern matching

Motivation: A palindrome is a string that reads the same forward and backward. Finding palindromic substructures is important in DNA, RNA or protein sequence analysis. We say that two strings of the same length are pal-equivalent if, for each possible centre, they have the same length of the maximal palindrome. Given a text T of length n and a pattern P of length m, we study the palindrome pattern matching problem that finds all indices i such that P and T[i-m+1:i] are pal-equivalent. Results: We first solve the online palindrome pattern matching problem in O(m²) preprocessing time and O(mn) query time using O(m²) space. We then extend the problem for multiple patterns and solve the online multiple palindrome pattern matching problem in O(mkM) preprocessing time and O(mkn+c) query time using O(mkM) space, where M is the sum of all pattern lengths, m_k is the longest pattern length and c is the number of pattern occurrences.