TY - JOUR

T1 - Asimpler and faster 1.5-approximation algorithm for sorting by transpositions

AU - Hartman, Tzvika

AU - Shamir, Ron

N1 - Funding Information:
Special thanks to Haim Kaplan, who pointed out the applicability of the data structure introduced in [18] for our algorithm, and to Elad Verbin for helpful discussions on this data structure. We thank Roded Sharan for fruitful discussions, and Vineet Bafna for help in understanding the complexity of the Bafna–Pevzner Algorithm [3]. This work was supported in part by the Israel Science Foundation (grant 309/02).

PY - 2006/2

Y1 - 2006/2

N2 - An important problem in genome rearrangements is sorting permutations by transpositions. The complexity of the problem is still open, and two rather complicated 1.5-approximation algorithms for sorting linear permutations are known (Bafna and Pevzner, 98 and Christie, 99). The fastest known algorithm is the quadratic algorithm of Bafna and Pevzner. In this paper, we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions. Hence, all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations. Our main result is a new O(n3/2√logn) 1.5-approximation algorithm, which is considerably simpler than the previous ones, and whose analysis is significantly less involved.

AB - An important problem in genome rearrangements is sorting permutations by transpositions. The complexity of the problem is still open, and two rather complicated 1.5-approximation algorithms for sorting linear permutations are known (Bafna and Pevzner, 98 and Christie, 99). The fastest known algorithm is the quadratic algorithm of Bafna and Pevzner. In this paper, we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions. Hence, all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations. Our main result is a new O(n3/2√logn) 1.5-approximation algorithm, which is considerably simpler than the previous ones, and whose analysis is significantly less involved.

KW - Computational biology

KW - Genome rearrangements

KW - Sorting permutations by transpositions

UR - http://www.scopus.com/inward/record.url?scp=84855205127&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2005.09.002

DO - 10.1016/j.ic.2005.09.002

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AN - SCOPUS:84855205127

VL - 204

SP - 275

EP - 290

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

IS - 2

ER -