Sorting by Reversals with Common Intervals

  • Martin Figeac
  • Jean-Stéphane Varré
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3240)


Studying rearrangements from gene order data is a standard approach in evolutionary analysis. Gene order data are usually modeled as signed permutations. The computation of the minimal number of reversals between two signed permutations produced a lot of literature during the last decade. Algorithms designed were first approximative, then polynomial and were further improved to give a linear one. Several extensions were investigated authorizing for example deletion or insertion of genes during the sorting process. We propose to revisit the ’sorting by reversals’ problem by adding constraints on allowed reversals. We do not allow to break conserved clusters of genes usually called Common Intervals. We show that this problem is NP-complete. Assuming special conditions, we propose a polynomial algorithm.

Omitted proofs are given as supplementary material at


Polynomial Algorithm Exponential Time Sorting Process Consecutive Block Identity Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Ajana, Y., Lefebvre, J.F., Tillier, E., El-Mabrouk, N.: Exploring the set of all minimal sequences of reversals - an application to test the replication-directed reversal hypothesis. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, p. 300. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bader, D., Moret, B., Yan, M.: A linear time algorithm for computing inversion distance between signed permutations with an expermimental study. Journal of (2000)Google Scholar
  3. 3.
    Bergeron, A., Chauve, C., Hartman, T., St-Onge, K.: On the properties of sequences of reversals that sort a signed permutation. In: Proceedings of JOBIM, JOBIM (2002)Google Scholar
  4. 4.
    Bergeron, A.: A very elementary presentation of the hannenhalli-pevzner theory. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, p. 106. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Caprara, A.: Sorting by reversals is difficult. ACM RECOMB (1997)Google Scholar
  6. 6.
    Cosner, M.E., Jansen, R.K., Moret, B.M.E., Raubeson, L.A., Wang, L., Warnow, T., Wyman, S.K.: An empirical comparison between bpanalysis and mpbe on the campanulaceae chloroplast genome dataset. Comparative Genomics (2000)Google Scholar
  7. 7.
    El-Mabrouk, N.: Sorting signed permutations by reversals and insertions/deletions of contiguous segments. Journal of Discrete Algorithms (2000)Google Scholar
  8. 8.
    Eriksen, N. (1+epsilon)-approximation of sorting by reversals and transpositions. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, p. 227. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Hannenhalli, S., Pevzner, P.: To cut.. or not to cut (applications of comparative physical maps in molecular evolution). In: Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 304–313 (1996)Google Scholar
  10. 10.
    Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: STOC (1995)Google Scholar
  11. 11.
    Heber, S., Stoye, J.: Algorithms for finding gene clusters. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, p. 252. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica 13, 180–210 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Pevzner, P., Tesler, G.: Transforming men into mice: the nadeau-taylor chromosomal breakage model revisited. In: RECOMB (2003)Google Scholar
  14. 14.
    Sankoff, D.: Short inversions and conserved gene clusters. Bioinformatics 18(10), 1305–1308 (2002)CrossRefGoogle Scholar
  15. 15.
    Uno, T., Yagiura, M.: Fast algorithms to enumerate all common intervals of two permutations. Algorithmica (2000)Google Scholar
  16. 16.
    Walter, M.E., Dias, Z., Meidanis, J.: Reversal and transposition distance of linear chromosomes. In: SPIRE (1998)Google Scholar
  17. 17.
    Wang, L.S., Warnow, T.: New polynomial time methods for whole-genome phylogeny reconstruction. In: Proc. 33rd Symp. on Theory of Comp. (2001) (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Figeac
    • 1
  • Jean-Stéphane Varré
    • 1
  1. 1.Laboratoire d’Informatique Fondamentale de LilleUniversité des sciences et technologies de LilleVilleneuve d’Ascq CedexFrance

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