Finding maximal 2-dimensional palindromes

This paper extends the problem of palindrome searching into a higher dimension, addressing two definitions of 2D palindromes. The first definition implies a square, while the second definition (also known as a centrosymmetric factor) can be any rectangular shape. We present a linear time algorithm for locating all maximal square 2D palindromes in a given 2D text. For the second definition of palindromes (rect2DP), we present two different algorithms. Given a text of size n x n, the first algorithm has time O(n(3)), which is linear in the worst case output size. The second algorithm has time O(n(2) logn + occ logn), where occis the number of maximal rect2D Pin the output. This provides a tradeoff in terms of output size; if the output size is small, the second algorithm is preferable, while the first would be more efficient if the output size is Theta (n(3)). (C) 2019 Elsevier Inc. All rights reserved.