A 1.5-approximation algorithm for sorting by transpositions and transreversals

Hartman, Tzvika; Sharan, Roded

doi:10.1016/j.jcss.2004.12.006

Cited by 43 publications

(41 citation statements)

References 16 publications

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“…Hence, our result closes the gap between the result of Hartman and Sharan [20] for the 1:1 proportion and that of Eriksen [15] for the 2:1 proportion. As the previous state of the art approximation algorithms for this problem, our algorithm proceeds by case analysis.…”

Section: Introductionsupporting

confidence: 87%

“…It has been proven by Hartman and Sharan [20] that sorting circular permutations is linearly equivalent to sorting linear permutations if yet another operation revrev is used that inverts two consecutive segments of the permutation. As long as the weights for transreversals and revrevs are the same, the proof also holds for sorting with weighted operations.…”

Section: Preliminariesmentioning

confidence: 99%

“…Alternative proofs for Lemmata 2.4 and 2.5 can be obtained by using the canonical labeling introduced in [11] and [20]. Lemma 2.7 (proven in [20]) Let a 1 and a 2 be two disjoint adjacent arcs in a configuration, so that there is at least one position in the configuration that is not covered by a 1 or a 2 .…”

Section: Lemma 22 (Proven In [19]) a 3-cycle Is T-oriented If And Onmentioning

confidence: 99%

“…Lemma 2.7 (proven in [20]) Let a 1 and a 2 be two disjoint adjacent arcs in a configuration, so that there is at least one position in the configuration that is not covered by a 1 or a 2 . Then there is a cycle with one reality-edge in a 1 or a 2 , and another reality-edge that is neither in a 1 nor in a 2 .…”

Section: Lemma 22 (Proven In [19]) a 3-cycle Is T-oriented If And Onmentioning

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: Introductionsupporting

confidence: 87%

Section: Preliminariesmentioning

confidence: 99%