English

On Approximability of Block Sorting

Computational Complexity 2011-10-06 v1 Data Structures and Algorithms

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.

Keywords

Cite

@article{arxiv.1110.0892,
  title  = {On Approximability of Block Sorting},
  author = {N. S. Narayanaswamy and Swapnoneel Roy},
  journal= {arXiv preprint arXiv:1110.0892},
  year   = {2011}
}
R2 v1 2026-06-21T19:15:18.598Z