Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Sorting permutations by block-interchanges
Information Processing Letters
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
(1+epsilon)-Approximation of Sorting by Reversals and Transpositions
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Reversals and Transpositions Over Finite Alphabets
SIAM Journal on Discrete Mathematics
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Multi-break rearrangements and chromosomal evolution
Theoretical Computer Science
Combinatorics of Genome Rearrangements
Combinatorics of Genome Rearrangements
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Genomic distance between two genomes, i.e., the smallest number of genome rearrangements required to transform one genome into the other, is often used as a measure of evolutionary closeness of the genomes in comparative genomics studies. However, in models that include rearrangements of significantly different "power" such as reversals (that are "weak" and most frequent rearrangements) and transpositions (that are more "powerful" but rare), the genomic distance typically corresponds to a transformation with a large proportion of transpositions, which is not biologically adequate. Weighted genomic distance is a traditional approach to bounding the proportion of transpositions by assigning them a relative weight α 1. A number of previous studies addressed the problem of computing weighted genomic distance with α ≤ 2. Employing the model of multi-break rearrangements on circular genomes, that captures both reversals (modelled as 2-breaks) and transpositions (modelled as 3-breaks), we prove that for α ∈ (1, 2), a minimumweight transformation may entirely consist of transpositions, implying that the corresponding weighted genomic distance does not actually achieve its purpose of bounding the proportion of transpositions. We further prove that for α ∈ (1, 2), the minimum-weight transformations do not depend on a particular choice of a from this interval. We give a complete characterization of such transformations and show that they coincide with the transformations that at the same time have the shortest length and make the smallest number of breakages in the genomes. Our results also provide a theoretical foundation for the empirical observation that for α