Title: Edit distances and factorisations of even permutations
Authors: Labarre, Anthony
Issue Date: Sep-2008
Publisher: Springer-Verlag
Host Document: Sixteenth Annual European Symposium on Algorithms (ESA) vol:5193 pages:635-646
Conference: European Symposium on Algorithms edition:16 location:Karlsruhe, Germany date:15-17 September 2008
Abstract: 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).
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Informatics Section

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