Sorting by Transpositions is Difficult

Abstract : In comparative genomics, a transposition is an operation that ex- changes 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 permuta- tions, called the S ORTING BY T RANSPOSITIONS problem (SBT), has been in- troduced 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 re- mained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the S ORTING BY T RANSPOSITIONS problem is NP-hard. As a corollary of our re- sult, we also prove that the following problem from [9] is NP-hard: given a per- mutation π, is it possible to sort π using db (π)/3 permutations, where db (π) is the number of breakpoints of π?
Liste complète des métadonnées

Cited literature [25 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00606223
Contributor : Guillaume Fertin <>
Submitted on : Tuesday, July 5, 2011 - 4:59:13 PM
Last modification on : Thursday, April 5, 2018 - 10:36:48 AM
Document(s) archivé(s) le : Thursday, October 6, 2011 - 2:27:08 AM

File

Transpositions-ICALP11.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00606223, version 1

Collections

Citation

Laurent Bulteau, Guillaume Fertin, Irena Rusu. Sorting by Transpositions is Difficult. 38th International Colloquium on Automata, Languages and Programming (ICALP 2011), 2011, Zürich, Switzerland. pp.654-665. ⟨hal-00606223⟩

Share

Metrics

Record views

223

Files downloads

112