ICALP 2011: Automata, Languages and Programming pp 654-665

# Sorting by Transpositions Is Difficult

• Laurent Bulteau
• Guillaume Fertin
• Irena Rusu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

## Abstract

In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years.

In this paper, we answer this long-standing open question by proving that the Sorting by Transpositions problem is NP-hard. As a corollary of our result, we also prove that the following problem from [10] is NP-hard: given a permutation π, is it possible to sort π using d b (π)/3 permutations, where d b (π) is the number of breakpoints of π?

## Keywords

Basic Block Boolean Variable Conjunctive Normal Form Boolean Formula Word Representation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Laurent Bulteau
• 1
• Guillaume Fertin
• 1
• Irena Rusu
• 1
1. 1.Laboratoire d’Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241Université de NantesNantes Cedex 3France