A quadratic time 2-approximation algorithm for block sorting

Authors:
Wolfgang W. Bein;Lawrence L. Larmore;Linda Morales;I. Hal Sudborough
Affiliations:
Center for the Advanced Study of Algorithms, School of Computer Science, University of Nevada, Las Vegas, NV 89154, USA;Center for the Advanced Study of Algorithms, School of Computer Science, University of Nevada, Las Vegas, NV 89154, USA;Department of Computer Science, University of Texas at Dallas Richardson, TX 75083, USA;Department of Computer Science, University of Texas at Dallas Richardson, TX 75083, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

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(n^2). 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(n^2) 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.