2-具有$k$不匹配的维回文

摘要：

本文将二维回文搜索问题推广到近似匹配领域。使用汉明距离作为度量，我们搜索允许多达$k$不匹配的2D回文。我们考虑两种不同的定义的二维回文，并描述有效的算法，他们都。第一个定义意味着正方形，而第二个定义（也称为\emph{centrosymmetric factor}）可以是任何矩形形状。给定大小为$n \times m$的文本，第一个算法的时间复杂度为$O(nm (\log m + \log n + k))$，第二个算法的时间复杂度为$O(nm(\log m + k) + occ)$，其中$occ$是输出的大小。

英文摘要：

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.

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