On Approximability of Block Sorting

N. S. Narayanaswamy; Swapnoneel Roy

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arXiv · 1110.0892

On Approximability of Block Sorting

N. S. Narayanaswamy·Swapnoneel Roy

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Abstract

Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation algorithms have been designed for the problem. But questions like whether a better approximation algorithm can be designed, and whether the problem is APX-Hard have been open for quite a while now. In this work we answer the latter question by proving Block Sorting to be Max-SNP-Hard (APX-Hard). The APX-Hardness result is based on a linear reduction of Max-3SAT to Block Sorting. We also provide a new lower bound for the problem via a new parametrized problem k-Block Merging.

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N. S. Narayanaswamy, Swapnoneel Roy. 2011-10-05. On Approximability of Block Sorting. https://arxiv.org/abs/1110.0892

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