Edit distances and factorisations of even permutations - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2008

Edit distances and factorisations of even permutations

Anthony Labarre

Résumé

A number of fields, including genome rearrangements and interconnection network design, are concerned with sorting permutations in "as few moves as possible", using a given set of allowed operations. These often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. The cycle graph of the permutation to sort is a fundamental tool in the theory of genome rearrangements. In this paper, we present an algebraic reinterpretation of the cycle graph as an even permutation, and show how to reformulate our sorting problems in terms of particular factorisations of the latter permutation. Using our framework, we recover known results in a simple and unified way, and obtain a new lower bound on the prefix transposition distance (where a prefix transposition displaces the initial segment of a permutation), which is shown to outperform previous results. Moreover, we use our approach to improve the best known lower bound on the prefix transposition diameter from 2n/3 to (3n+1)/(4).
Fichier principal
Vignette du fichier
esa2008.pdf (447.58 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-00728921 , version 1 (07-09-2012)

Identifiants

Citer

Anthony Labarre. Edit distances and factorisations of even permutations. Proceedings of the Sixteenth Annual European Symposium on Algorithms (ESA), Sep 2008, Germany. pp.635-646, ⟨10.1007/978-3-540-87744-8_53⟩. ⟨hal-00728921⟩
33 Consultations
222 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More