2-Dimensional Palindromes with $k$ Mismatches

Abstract

This paper extends the problem of 2-dimensional palindrome search into the area of approximate matching. Using the Hamming distance as the measure, we search for 2D palindromes that allow up to k mismatches. We consider two different definitions of 2D palindromes and describe efficient algorithms for both of them. The first definition implies a square, while the second definition (also known as a centrosymmetric factor ), can be any rectangular shape. Given a text of size n × m, the time complexity of the first algorithm is O(nm(log m + log n + k)) and for the second algorithm it is O(nm(log m + k) + occ) where occ is the size of the output.