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A 1.375-Approximation Algorithm for Sorting by Transpositions
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2006 (English)In: IEEE/ACM Transactions on Computational Biology & Bioinformatics, ISSN 1545-5963, E-ISSN 1557-9964, Vol. 3, no 4, 369-379 p.Article in journal (Refereed) Published
Abstract [en]

Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a 10-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper, we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: We improve the lower bound for the transposition diameter of the symmetric group and determine the exact transposition diameter of simple permutations.

Place, publisher, year, edition, pages
2006. Vol. 3, no 4, 369-379 p.
Keyword [en]
computational biology, genome rearrangements, sorting permutations by transpositions
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-6354DOI: 10.1109/TCBB.2006.44ISI: 000241720700006Scopus ID: 2-s2.0-33845654494OAI: oai:DiVA.org:kth-6354DiVA: diva2:11043
Conference
5th International Workshop on Algorithms in Bioinformatics (WABI 2005) Mallorca, Spain, OCT 03-06, 2005
Note

QC 20110121 QC 20110927.

Available from: 2006-11-15 Created: 2006-11-15 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Computational problems in evolution: Multiple alignment, genome rearrangements, and tree reconstruction
Open this publication in new window or tab >>Computational problems in evolution: Multiple alignment, genome rearrangements, and tree reconstruction
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Reconstructing the evolutionary history of a set of species is a fundamental problem in biology. This thesis concerns computational problems that arise in different settings and stages of phylogenetic tree reconstruction, but also in other contexts. The contributions include:

• A new distance-based tree reconstruction method with optimal reconstruction radius and optimal runtime complexity. Included in the result is a greatly simplified proof that the NJ algorithm also has optimal reconstruction radius. (co-author Jens Lagergren)

• NP-hardness results for the most common variations of Multiple Alignment. In particular, it is shown that SP-score, Star Alignment, and Tree Alignment, are NP hard for all metric symbol distances over all binary or larger alphabets.

• A 1.375-approximation algorithm for Sorting By Transpositions (SBT). SBT is the problem of sorting a permutation using as few block-transpositions as possible. The complexity of this problem is still open and it was a ten-year-old open problem to improve the best known 1.5-approximation ratio. The 1.375-approximation algorithm is based on a new upper bound on the diameter of 3-permutations. Moreover, a new lower bound on the transposition diameter of the symmetric group is presented and the exact transposition diameter of simple permutations is determined. (co-author Tzvika Hartman)

• Approximation, fixed-parameter tractable, and fast heuristic algorithms for two variants of the Ancestral Maximum Likelihood (AML) problem: when the phylogenetic tree is known and when it is unknown. AML is the problem of reconstructing the most likely genetic sequences of extinct ancestors along with the most likely mutation probabilities on the edges, given the phylogenetic tree and sequences at the leafs. (co-author Tamir Tuller)

• An algorithm for computing the number of mutational events between aligned DNA sequences which is several hundred times faster than the famous Phylip packages. Since pairwise distance estimation is a bottleneck in distance-based phylogeny reconstruction, the new algorithm improves the overall running time of many distancebased methods by a factor of several hundred. (co-author Jens Lagergren)

Place, publisher, year, edition, pages
Stockholm: KTH, 2006. iv, 54 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 06/22--SE
Keyword
Distance Methods, Tree reconstruction, Sorting by Transpositions, multiple alignment, ancestral sequences
National Category
Computer Science
Identifiers
urn:nbn:se:kth:diva-4170 (URN)978-91-7178-511-4 (ISBN)
Public defence
2007-01-15, FA32, Albanova, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20110121Available from: 2006-11-15 Created: 2006-11-15 Last updated: 2011-01-21Bibliographically approved

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