The block sorting problem is the problem of minimizing the number of steps to sort a list of distinct items, where a sublist of items which are already in sorted order, called a block, can be moved in one step. We give an approximation algorithm for the block sorting problem with an approximation ratio of 2 and run time O (n2). The approximation algorithm is based on the related concept of block deletion. We show that finding an optimum block deletion sequence can be done in O (n2) time, even though block sorting is known to be N P-hard. Block sorting has importance in connection with optical character recognition (OCR) and is related to transposition sorting in computational biology. © 2009.
Bein, W. W., Larmore, L. L., Morales, L., & Sudborough, I. H. (2009). A quadratic time 2-approximation algorithm for block sorting. Theoretical Computer Science, 410(8–10), 711–717. https://doi.org/10.1016/j.tcs.2008.10.022