Rearrangement Models and Single-Cut Operations

  • Paul Medvedev
  • Jens Stoye
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5817)


There have been many widely used genome rearrangement models, such as reversals, Hannenhalli-Pevzner, and double-cut and join. Though each one can be precisely defined, the general notion of a model remains undefined. In this paper, we give a formal set-theoretic definition, which allows us to investigate and prove relationships between distances under various existing and new models. We also initiate the formal study of single-cut operations by giving a linear time algorithm for the distance problem under a new single-cut and join model.


Genome Rearrangement Synteny Block Circular Chromosome Linear Chromosome Distance Problem 
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  1. 1.
    Adam, Z., Sankoff, D.: The ABCs of MGR with DCJ. Evol. Bioinform. 4, 69–74 (2008)Google Scholar
  2. 2.
    Alekseyev, M.A., Pevzner, P.A.: Are there rearrangement hotspots in the human genome? PLoS Comput. Biol. 3(11), e209 (2007)CrossRefGoogle Scholar
  3. 3.
    Alekseyev, M.A., Pevzner, P.A.: Whole genome duplications, multi-break rearrangements, and genome halving problem. In: SODA, pp. 665–679 (2007)Google Scholar
  4. 4.
    Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comp. Biol. 8(5), 483–491 (2001)CrossRefGoogle Scholar
  5. 5.
    Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 163–173. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Bergeron, A., Mixtacki, J., Stoye, J.: HP distance via double cut and join distance. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 56–68. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Bergeron, A., Mixtacki, J., Stoye, J.: On computing the breakpoint reuse rate in rearrangement scenarios. In: Nelson, C.E., Vialette, S. (eds.) RECOMB-CG 2008. LNCS (LNBI), vol. 5267, pp. 226–240. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Cohen, D.S., Blum, M.: On the problem of sorting burnt pancakes. Discr. Appl. Math. 61(2), 105–120 (1995)CrossRefGoogle Scholar
  9. 9.
    Dobzhansky, T., Sturtevant, A.H.: Inversions in the chromosomes of Drosophila Pseudoobscura. Genetics 23, 28–64 (1938)PubMedPubMedCentralGoogle Scholar
  10. 10.
    Feijão, P., Meidanis, J.: SCJ: A novel rearrangement operation for which sorting, genome median and genome halving problems are easy. In: Salzberg, S.L., Warnow, T. (eds.) WABI 2009. LNCS (LNBI), vol. 5724, pp. 85–96. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Gates, W., Papadimitiou, C.: Bounds for sorting by prefix reversals. Discr. Math. 27, 47–57 (1979)CrossRefGoogle Scholar
  12. 12.
    Hannenhalli, S., Pevzner, P.A.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proceedings of FOCS 1995, pp. 581–592. IEEE Press, Los Alamitos (1995)Google Scholar
  13. 13.
    Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. J. ACM 46(1), 1–27 (1999); First appeared in STOC 1995 ProceedingsCrossRefGoogle Scholar
  14. 14.
    Jean, G., Nikolski, M.: Genome rearrangements: a correct algorithm for optimal capping. Inf. Process. Lett. 104, 14–20 (2007)CrossRefGoogle Scholar
  15. 15.
    Lin, Y., Moret, B.M.E.: Estimating true evolutionary distances under the DCJ model. Bioinformatics 24, i114–i122 (2008); Proceedings of ISMB 2008CrossRefGoogle Scholar
  16. 16.
    Ma, J., Zhang, L., Suh, B.B., Raney, B.J., Burhans, R.C., Kent, W.J., Blanchette, M., Haussler, D., Miller, W.: Reconstructing contiguous regions of an ancestral genome. Genome Research 16(12), 1557–1565 (2006)CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Meidanis, J., Walter, M.E.M.T., Dias, Z.: Reversal distance of signed circular chromosomes. In: Technical Report IC–00-23. Institute of Computing, University of Campinas (2000)Google Scholar
  18. 18.
    Mixtacki, J.: Genome halving under DCJ revisited. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 276–286. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Nadeau, J.H., Taylor, B.A.: Lengths of chromosomal segments conserved since divergence of man and mouse. Proc. Natl. Acad. Sci. USA 81, 814–818 (1984)CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Ozery-Flato, M., Shamir, R.: Two notes on genome rearrangements. J. Bioinf. Comput. Biol. 1(1), 71–94 (2003)CrossRefGoogle Scholar
  21. 21.
    Pevzner, P.A., Tesler, G.: Transforming men into mice: the Nadeau-Taylor chromosomal breakage model revisited. In: Proceedings of RECOMB 2003, pp. 247–256 (2003)Google Scholar
  22. 22.
    Sankoff, D.: Edit distances for genome comparison based on non-local operations. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 121–135. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  23. 23.
    Sankoff, D., Cedergren, R., Abel, Y.: Genomic divergence through gene rearrangement. In: Doolittle, R.F. (ed.) Molecular Evolution: Computer Analysis of Protein and Nucleic Acid Sequences, Meth. Enzymol., ch. 26, vol. 183, pp. 428–438. Academic Press, San Diego (1990)Google Scholar
  24. 24.
    Sankoff, D., Trinh, P.: Chromosomal breakpoint reuse in genome sequence rearrangement. J. of Comput. Biol. 12(6), 812–821 (2005)CrossRefGoogle Scholar
  25. 25.
    Tannier, E., Bergeron, A., Sagot, M.-F.: Advances on sorting by reversals. Discr. Appl. Math. 155(6-7), 881–888 (2007)CrossRefGoogle Scholar
  26. 26.
    Tesler, G.: Efficient algorithms for multichromosomal genome rearrangements. J. Comput. Syst. Sci. 65(3), 587–609 (2002)CrossRefGoogle Scholar
  27. 27.
    Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21(16), 3340–3346 (2005)CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paul Medvedev
    • 1
  • Jens Stoye
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoCanada
  2. 2.Technische FakultätUniversität BielefeldGermany

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