A simpler and faster 1.5-approximation algorithm for sorting by transpositions

Hartman, Tzvika; Shamir, Ron

doi:10.1016/j.ic.2005.09.002

Cited by 51 publications

(30 citation statements)

References 16 publications

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“…The configurations consisting solely of 3-cycles have already been described in [19] and [20]. A careful inspection of the starting sequences provided there reveals that these sequences also work in our case.…”

Section: The Algorithm For Simple Permutationssupporting

confidence: 53%

“…A permutation is called simple if it contains no long cycles. According to [18][19][20][21], there is a padding algorithm that transforms any permutation π into a simple permutatioñ π. Each transformation step increases n and c odd by 1, and leaves c even unchanged.…”

Section: Transformation Into Simple Permutationsmentioning

confidence: 99%

“…However, some of the sequences are only optimal for the unweighted case, and others are rather difficult to implement, so we improved these sequences. For all cases where we use the starting sequences provided in [19] or [20], we will refer to the source of the starting sequences. For all other cases, we will provide our own starting sequences.…”

Section: The Algorithm For Simple Permutationsmentioning

confidence: 99%

“…The first two of these sequences are taken from [19] and [20]. For the last case, we could improve the sequence by increasing the number of reversals while decreasing the number of transpositions.…”

Section: The Algorithm For Simple Permutationsmentioning

confidence: 99%

“…Hartman and Sharan provided a very efficient 1.5-approximation algorithm for this case [20], extending a 1.5-approximation algorithm for sorting by transpositions only [19]. However, the drawback of their algorithm is that it applies only to the case in which reversals and transpositions are weighted equally (called the unweighted case in this paper).…”

Section: Introductionmentioning

confidence: 99%

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Sorting by Weighted Reversals, Transpositions, and Inverted Transpositions

Bader

Ohlebusch

2006

Lecture Notes in Computer Science

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During evolution, genomes are subject to genome rearrangements that alter the ordering and orientation of genes on the chromosomes. If a genome consists of a single chromosome (like mitochondrial, chloroplast, or bacterial genomes), the biologically relevant genome rearrangements are (1) inversions-also called reversals-where a section of the genome is excised, reversed in orientation, and reinserted and (2) transpositions, where a section of the genome is excised and reinserted at a new position in the genome; if this also involves an inversion, one speaks of an inverted transposition. To reconstruct ancient events in the evolutionary history of organisms, one is interested in finding an optimal sequence of genome rearrangements that transforms a given genome into another genome. It is well known that this problem is equivalent to the problem of "sorting" a signed permutation into the identity permutation. In this paper, we provide a 1.5-approximation algorithm for sorting by weighted reversals, transpositions and inverted transpositions for biologically realistic weights.

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Section: The Algorithm For Simple Permutationssupporting

confidence: 53%