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Faster algorithms for sorting by transpositions and sorting by block interchanges

Published: 01 August 2007 Publication History

Abstract

In this article, we present a new data structure, called the permutation tree, to improve the running time of sorting permutation by transpositions and sorting permutation by block interchanges. The existing 1.5-approximation algorithm for sorting permutation by transpositions has time complexity O(n3/2logn). By means of the permutation tree, we can improve this algorithm to achieve time complexity O(nlogn). We can also improve the algorithm for sorting permutation by block interchanges to take its time complexity from O(n2) down to O(nlogn).

References

[1]
Bader, D. A., Moret, B. M. E., and Yan, M. 2001. A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comput. Biol. 8, 5, 483--491.
[2]
Bafna, V., and Pevzner, P. A. 1998. Sorting by transpositions. SIAM J. Discrete Math. 11, 2, 224--240.
[3]
Bafna, V., and Pevzner, P. A. 1996. Genome rearrangements and sorting by reversals. SIAM J. Comput. 25, 2, 272--289.
[4]
Bergeron, A. 2005. A very elementary presentation of the hannenhalli-pevzner theory. Discrete Appl. Math. 146, 2, 134--145.
[5]
Berman, P., Hannenhalli, S., and Karpinski, M. 2002. 1.375-approximation algorithm for sorting by reversals. In Proceedings of the 10th Annual European Symposium on Algorithms (Rome). Lecture Notes in Computer Science, vol. 2461. Springer, 200--210.
[6]
Caprara, A. 1999. Sorting permutations by reversals and Eulerian cycle decompositions. SIAM J. Discrete Math. 12, 1, 91--110.
[7]
Christie, D. A. 1999. Genome rearrangement problems. Ph.D. thesis, University of Glasgow.
[8]
Christie, D. A. 1998. A 3/2-approximation algorithm for sorting by reversals. In Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Society for Industrial and Applied Mathematics, Philadelphia, PA, 244--252.
[9]
Christie, D. A. 1996. Sorting permutations by block-interchanges. Inf. Process. Lett. 60, 4, 165--169.
[10]
Elias, I., and Hartman, T. 2006. A 1.375-approximation algorithm for sorting by transpositions. IEEE/ACM Trans. Comput. Biol. Bioinf. 3, 4, 369--379.
[11]
Eriksen, N. 2002. (1 + ε)-approximation of sorting by reversals and transpositions. Theor. Comput. Sci. 289, 1, 517--529.
[12]
Eriksson, H., Eriksson, K., Karlander, J., Svensson, L., and Wastlund, J. 2001. Sorting a bridge hand. Discrete Math. 241, 1--3, 289--300.
[13]
Gu, Q.-P., Peng, S., and Sudborough, H. 1999. A 2-approximation algorithm for genome rearrangements by reversals and transpositions. Theor. Comput. Sci. 210, 2, 327--339.
[14]
Hannenhalli, S., and Pevzner, P. A. 1999. Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. J. ACM 46, 1, 1--27.
[15]
Hartman, T., and Shamir, R. 2006. A simpler and faster 1.5-approximation algorithm for sorting by transpositions. Inf. Comput. 204, 2, 275--290.
[16]
Hartman, T., and Shamir, R. 2003. A simpler 1.5-approximation algorithm for sorting by transpositions. In Proceedings of the 14th Annual Symposium on Combinatorial Pattern Matching (Morelia, Michoacn, Mexico). Lecture Notes in Computer Science, vol. 2676. Springer, 156--169.
[17]
Hoot, S. B., and Palmer, J. D. 1994. Structural rearrangements, including parallel inversions, within the chloroplast genome of anemone and related genera. J. Molecular Evolution 38, 3, 274--281.
[18]
Kaplan, H., and Verbin, E. 2003. Efficient data structures and a new randomized approach for sorting signed permutatins by reversals. In Proceedings of the 14th Annual Symposium on Combinatorial Pattern Matching (Morelia, Michoacn, Mexico). Lecture Notes in Computer Science, vol. 2676. Springer, 170--185.
[19]
Lin, G.-H., and Xue, G. 2001. Signed genome rearrangement by reversals and transpositions: Models and approximations. Theor. Comput. Sci. 259, 1-2, 513--531.
[20]
Lin, Y., Lu, C., Chang, H., and Tang, C. 2005. An efficient algorithm for sorting by block-interchanges and its application to the evolution of vibrio species. J. Comput. Biol. 12, 1, 102--112.
[21]
Palmer, J. D., and Herbon, L. A. 1986. Tricircular mitochondrial genomes of brassica and raphanus: Reversal of repeat configurations by inversion. Nucleic Acids Res. 14, 24, 9755--9765.
[22]
Sleator, D. D., and Tarjan, R. E. 1985. Self-Adjusting binary search trees. J. ACM 32, 3, 652--686.
[23]
Walter, M. E. T., Curado, L. R. A. F., and Oliveira, A. G. 2003. Working on the problem of sorting by transpositions on genome rearrangements. In Proceedings of the 14th Annual Symposium on Combinatorial Pattern Matching (Morelia, Michoacn, Mexico). Lecture Notes in Computer Science, vol. 2676. Springer, 372--383.

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cover image ACM Transactions on Algorithms
ACM Transactions on Algorithms  Volume 3, Issue 3
August 2007
216 pages
ISSN:1549-6325
EISSN:1549-6333
DOI:10.1145/1273340
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 August 2007
Published in TALG Volume 3, Issue 3

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Author Tags

  1. Block interchange
  2. genome
  3. permutation
  4. time complexity
  5. transposition
  6. tree

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  • (2024)On an Algorithm for Sorting by Strip Swaps Using Cycle Graphs2024 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)10.1109/BIBM62325.2024.10822561(5355-5363)Online publication date: 3-Dec-2024
  • (2023)Reversal and Indel Distance With Intergenic Region InformationIEEE/ACM Transactions on Computational Biology and Bioinformatics10.1109/TCBB.2022.321561520:3(1628-1640)Online publication date: 1-May-2023
  • (2023)On Sorting by Flanked TranspositionsBioinformatics Research and Applications10.1007/978-981-99-7074-2_23(292-311)Online publication date: 9-Oct-2023
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