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New approximations for block sorting

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An Erratum to this article was published on 21 January 2017

Abstract

We develop, present, and analyze a simple, new 2-approximation algorithm for block sorting in which we use a newly introduced combinatorial structure called an ordered pair. Our algorithm achieves the best known approximation ratio of 2 , the tightest known upper bound in terms of the number of block moves needed for block sorting.

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References

  • Bafna V, Pavel PA (1998) Sorting by transpositions. SIAM J Discrete Math

  • Bafna V, Pevzner PA (1996) Genome rearrangements and sorting by reversals. SIAM J Comput 25(2):272–289. doi:10.1137/S0097539793250627

    Article  MathSciNet  MATH  Google Scholar 

  • Bein WW, Larmore LL, Latifi S, Sudborough IH (2003) Block sorting is hard. Int J Found Comput Sci 14(03):425–437

    Article  MathSciNet  MATH  Google Scholar 

  • Bein WW, Larmore LL, Morales L, Sudborough IH (2009) A quadratic time 2-approximation algorithm for block sorting. Theor Comput Sci 410(8):711–717

    Article  MathSciNet  MATH  Google Scholar 

  • Bulteau L, Fertin G, Rusu I (2001) Sorting by transpositions is difficult. In: Proceedings of the 38th international colloquim conference on automata, languages and programming—volume part I, ICALP’11. Springer, Berlin, pp 654–665. http://dl.acm.org/citation.cfm?id=2027127.2027197

  • Bulteau L, Fertin G, Rusu I (2012) Pancake flipping is hard. In: Proceedings of the 37th international conference on mathematical foundations of computer science, MFCS’12. Springer, Berlin, pp 247–258. doi:10.1007/978-3-642-32589-2_24

  • Caprara A (1997) Sorting by reversals is difficult. In: Proceedings of the first annual international conference on computational molecular biology, RECOMB ’97. ACM, New York, NY, USA, pp 75–83. doi:10.1145/267521.267531, http://doi.acm.org/10.1145/267521.267531

  • Christie D, Irving R (2001) Sorting strings by reversals and by transpositions. SIAM J Discrete Math 14(2):193–206. doi:10.1137/S0895480197331995

    Article  MathSciNet  MATH  Google Scholar 

  • Christie DA (1996) Sorting permutations by block-interchanges. Inf Process Lett 60(4):165–169

    Article  MathSciNet  MATH  Google Scholar 

  • Christie DA (1999) Genome rearrangement problems. Ph.D. thesis

  • Elias I, Hartman T (2006) A 1.375-approximation algorithm for sorting by transpositions. IEEE/ACM Trans Comput Biol Bioinform 3(4):369–379. doi:10.1109/TCBB.2006.44

    Article  Google Scholar 

  • Firoz JS, Hasan M, Khan AZ, Rahman MS (2011) The 1.375 approximation algorithm for sorting by transpositions can run in o (n log n) time. J Comput Biol 18(8):1007–1011

    Article  MathSciNet  MATH  Google Scholar 

  • Gates WH, Papadimitriou CH (1979) Bounds for sorting by prefix reversal. Discrete Math 27(1):47–57

    Article  MathSciNet  MATH  Google Scholar 

  • Gu QP, Peng S, Sudborough H (1999) A 2-approximation algorithm for genome rearrangements by reversals and transpositions. Theor Comput Sci 210(2):327–339

    Article  MathSciNet  MATH  Google Scholar 

  • Hannenhalli S, Pevzner PA (1999) Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. J ACM 46(1):1–27. doi:10.1145/300515.300516. http://doi.acm.org/10.1145/300515.300516

  • Hartman T, Shamir R (2006) A simpler and faster 1.5-approximation algorithm for sorting by transpositions. Inf Comput 204(2):275–290

    Article  MathSciNet  MATH  Google Scholar 

  • Huang J, Roy S (2014) On sorting under special transpositions. In: 2014 IEEE international conference on bioinformatics and bioengineering (BIBE), pp 325–328

  • Lin YC, Lu CL, Chang HY, Tang CY (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

    Article  Google Scholar 

  • Mahajan M, Rama R, Raman V, Vijaykumar S (2006) Approximate block sorting. Int J Found Comput Sci 17(02):337–355

    Article  MathSciNet  MATH  Google Scholar 

  • Mira C, Meidanis J (2007) Sorting by block-interchanges and signed reversals. In: Fourth International Conference on information technology, 2007, ITNG’07, pp 670–676

  • Narayanaswamy N, Roy S (2015) Block sorting is apx-hard. In: Algorithms and complexity. Springer, pp 377–389

  • Palmer JD, Herbon LA (1988) Plant mitochondrial dna evolved rapidly in structure, but slowly in sequence. J Mol Evol 28(1–2):87–97

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers of an earlier version of this paper. Their constructive remarks helped improve the quality of the paper.

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Authors and Affiliations

  1. University of North Florida, 1 UNF Drive, Jacksonville, FL, USA

    J. Huang, S. Roy & A. Asaithambi

Authors
  1. J. Huang
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  2. S. Roy
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  3. A. Asaithambi
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Corresponding author

Correspondence to S. Roy.

Additional information

A preliminary version of this work appeared in the proceedings of BIBE 2014.

An erratum to this article is available at http://dx.doi.org/10.1007/s13721-016-0145-2.

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Huang, J., Roy, S. & Asaithambi, A. New approximations for block sorting. Netw Model Anal Health Inform Bioinforma 5, 6 (2016). https://doi.org/10.1007/s13721-016-0113-x

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