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 \emph{centrosymmetric factor}), can be any rectangular shape. Given a text of size $n \times m$, 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.