A quadratic time 2-approximation algorithm for block sorting

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 NP-hard. Block sorting has importance in connection with optical character recognition (OCR) and is related to transposition sorting in computational biology.