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Settling the Intractability of Multiple Alignment
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2006 (English)In: Journal of Computational Biology, ISSN 1066-5277, E-ISSN 1557-8666, Vol. 13, no 7, 1323-1339 p.Article in journal (Refereed) Published
Abstract [en]

Multiple alignment is a core problem in computational biology that has received much attention over the years, both in the line of heuristics and hardness results. In most expositions of the problem it is referred to as NP-hard and references are given to one of the available hardness results. However, previous to this paper not even the most elementary variation of the problem, multiple alignment under the unit metric, had been proved hard. The aim of this paper is to settle the NP-hardness of the most common variations of multiple alignment. The following variations are shown NP-hard for all metrics over binary or larger alphabets: Multiple Alignment with SP-score, Star Alignment, and Tree Alignment ( for a given phylogeny). In addition, NP-hardness results are provided for Consensus Patterns and Substring Parsimony.

Place, publisher, year, edition, pages
2006. Vol. 13, no 7, 1323-1339 p.
Keyword [en]
multiple alignment, NP-hard, SP-score, star alignment, tree alignment, consensus patterns, substring parsimony
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-6352ISI: 000241414800004Scopus ID: 2-s2.0-33846197539OAI: oai:DiVA.org:kth-6352DiVA: diva2:11041
Note
QC 20110121Available from: 2006-11-15 Created: 2006-11-15 Last updated: 2011-01-21Bibliographically 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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Scopushttp://www.liebertonline.com/doi/abs/10.1089/cmb.2006.13.1323

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