Year

2015

Season

Summer

Paper Type

Master's Thesis

College

College of Computing, Engineering & Construction

Degree Name

Master of Science in Computer and Information Sciences (MS)

Department

Computing

NACO controlled Corporate Body

University of North Florida. School of Computing

First Advisor

Dr. Swapnoneel Roy

Second Advisor

Dr. Ching-Hua Chuan

Third Advisor

Dr. William F. Klostermeyer

Department Chair

Dr. Asai Asaithambi

College Dean

Dr. Mark A. Tumeo

Abstract

The research in this thesis is focused on the problem of Block Sorting, which has applications in Computational Biology and in Optical Character Recognition (OCR). A block in a permutation is a maximal sequence of consecutive elements that are also consecutive in the identity permutation. BLOCK SORTING is the process of transforming an arbitrary permutation to the identity permutation through a sequence of block moves. Given an arbitrary permutation π and an integer m, the Block Sorting Problem, or the problem of deciding whether the transformation can be accomplished in at most m block moves has been shown to be NP-hard. After being known to be 3-approximable for over a decade, block sorting has been researched extensively and now there are several 2-approximation algorithms for its solution. This work introduces new structures on a permutation, which are called runs and ordered pairs, and are used to develop two new approximation algorithms. Both the new algorithms are 2-approximation algorithms, yielding the approximation ratio equal to the current best. This work also includes an analysis of both the new algorithms showing they are 2-approximation algorithms.

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