An algorithm to enumerate sorting reversals for signed permutations

Siepel, A. C. (2003) An algorithm to enumerate sorting reversals for signed permutations. J Comput Biol, 10 (3-4). pp. 575-97. ISSN 1066-5277 (Print)1066-5277

DOI: 10.1089/10665270360688200


The rearrangement distance between single-chromosome genomes can be estimated as the minimum number of inversions required to transform the gene ordering observed in one into that observed in the other. This measure, known as "inversion distance," can be computed as the reversal distance between signed permutations. During the past decade, much progress has been made both on the problem of computing reversal distance and on the related problem of finding a minimum-length sequence of reversals, which is known as "sorting by reversals." For most problem instances, however, many minimum-length sequences of reversals exist, and in the absence of auxiliary information, no one is of greater value than the others. The problem of finding all minimum-length sequences of reversals is thus a natural generalization of sorting by reversals, yet it has received little attention. This problem reduces easily to the problem of finding all "sorting reversals" of one permutation with respect to another - that is, all reversals rho such that, if rho is applied to one permutation, then the reversal distance of that permutation from the other is decreased. In this paper, an efficient algorithm is derived to solve the problem of finding all sorting reversals, and experimental results are presented indicating that, while the new algorithm does not represent a significant improvement in asymptotic terms (it takes O(n(3)) time, for permutations of size n; the problem can now be solved by brute force in Theta(n(3)) time), it performs dramatically better in practice than the best known alternative. An implementation of the algorithm is available at

Item Type: Paper
Uncontrolled Keywords: *Algorithms Chromosome Mapping/*methods Computational Biology/*methods Data Interpretation, Statistical *Evolution, Molecular Gene Order Sequence Analysis, DNA/methods
Subjects: bioinformatics
bioinformatics > computational biology
CSHL Authors:
Communities: CSHL labs > Siepel lab
Depositing User: Matt Covey
Date Deposited: 12 Jan 2015 20:51
Last Modified: 12 Jan 2015 20:51
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