A simple framework on sorting permutations

Matrix Tightness: A Linear-Algebraic Framework for Sorting by Transpositions

We study the problems of sorting signed permutations by reversals (SBR) and sorting unsigned permutations by transpositions (SBT), which are central problems in computational molecular biology. While a polynomial-time solution for SBR is known, the computational complexity of SBT has been open for more than a decade and is considered a major open problem. In the first efficient solution of SBR,...

Fast Algorithms for Transforming Back and Forth between a Signed Permutation and Its Equivalent Simple Permutation

The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. A...

Virtual Memory for Data-Parallel Computing

This thesis explores several issues that arise in the design and implementation of virtual-memory systems for data-parallel computing. Chapter 1 presents an overview of virtual memory for data-parallel computing. The chapter lists some applications that may benefit from large address spaces in a data-parallel model. It also describes the view of virtual memory for data-parallel computing used i...

Lower bounding edit distances between permutations

A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in as few moves as possible, using a given set of allowed operations, or computing the number of moves the sorting process requires, often referred to as the distance of the permutation. These operations often act on just one or tw...

A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals