On the Similarity of Sets of Permutations and Its Applications to Genome Comparison

  • Anne Bergeron
  • Jens Stoye
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2697)


The comparison of genomes with the same gene content relies on our ability to compare permutations, either by measuring how much they differ, or by measuring how much they are alike. With the notable exception of the breakpoint distance, which is based on the concept of conserved adjacencies, measures of distance do not generalize easily to sets of more than two permutations. In this paper, we present a basic unifying notion, conserved intervals, as a powerful generalization of adjacencies, and as a key feature of genome rearrangement theories. We also show that sets of conserved intervals have elegant nesting and chaining properties that allow the development of compact graphic representations, and linear time algorithms to manipulate them.


Genome Rearrangement Maximal Chain Interval Distance Ancestral Genome 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. Ajana, J.-F. Lefebvre, E. R. M. Tillier, and N. El-Mabrouk. Exploring the set of all minimal sequences of reversals — an application to test the replication-directed reversal hypothesis. In Proc. WABI 2002, volume 2452 of LNCS, pages 300–315. Springer Verlag, 2002.Google Scholar
  2. 2.
    D. A. Bader, B. M. E. Moret, and M. Yan. A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comp. Biol., 8(5):483–492, 2001.CrossRefGoogle Scholar
  3. 3.
    V. Bafna and P. A. Pevzner. Sorting by transpositions. SIAM J. Disc. Math., 11(2):224–240, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    A. Bergeron, S. Heber, and J. Stoye. Common intervals and sorting by reversals: A marriage of necessity. Bioinformatics, 18(Suppl. 2):S54–S63, 2002. (Proc. ECCB 2002).Google Scholar
  5. 5.
    A. Bergeron and J. Stoye. On the similarity of sets of permutations and its application to genome comparison. Report 2003-01, Technische Fakultät der Universität Bielefeld, 2003. (Available at Scholar
  6. 6.
    M. Blanchette, T. Kunisawa, and D. Sankoff. Gene order breakpoint evidence in animal mitochondrial phylogeny. J. Mol. Evol., 49(2):193–203, 1999.CrossRefGoogle Scholar
  7. 7.
    J. L. Boore. Mitochondrial gene arrangement source guide. Scholar
  8. 8.
    K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci., 13(3):335–379, 1976.zbMATHMathSciNetGoogle Scholar
  9. 9.
    G. Bourque and P. A. Pevzner. Genome-scale evolution: Reconstructing gene orders in the ancestral species. Genome Res., 12(1):26–36, 2002.Google Scholar
  10. 10.
    D. A. Christie. Genome Rearrangement Problems. PhD thesis, The University of Glasgow, 1998.Google Scholar
  11. 11.
    S. Hannenhalli and P. A. Pevzner. Transforming men into mice (polynomial algorithm for genomic distance problem). In Proc. FOCS 1995, pages 581–592. IEEE Press, 1995.Google Scholar
  12. 12.
    S. Hannenhalli and P. A. Pevzner. Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. J. ACM, 46(1):1–27, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    S. Heber and J. Stoye. Finding all common intervals of k permutations. In Proc. CPM 2001, volume 2089 of LNCS, pages 207–218. Springer Verlag, 2001.Google Scholar
  14. 14.
    H. Kaplan, R. Shamir, and R. E. Tarjan. A faster and simpler algorithm for sorting signed permutations by reversals. SIAM J. Computing, 29(3):880–892, 1999.CrossRefMathSciNetGoogle Scholar
  15. 15.
    J. D. Kececioglu and D. Sankoff. Efficient bounds for oriented chromosome inversion distance. In Proc. CPM 1994, volume 807 of LNCS, pages 307–325. Springer Verlag, 1994.Google Scholar
  16. 16.
    B. Larget, J. Kadane, and D. Simon. A Markov chain Monte Carlo approach to reconstructing ancestral genome rearrangements. Technical report, Carnegie Mellon University, Pittsburgh, 2002.Google Scholar
  17. 17.
    B. M. E. Moret, A. C. Siepel, J. Tang, and T. Liu. Inversion medians outperform breakpoint medians in phylogeny reconstruction from gene-order data. In Proc. WABI 2002, volume 2452 of LNCS, pages 521–536. Springer Verlag, 2002.Google Scholar
  18. 18.
    M. Ozery-Flato and R. Shamir. Two notes on genome rearrangements. J. Bioinf. Comput. Biol., to appear.Google Scholar
  19. 19.
    D. Sankoff. Short inversions and conserved gene clusters. Bioinformatics, 18(10):1305–1308, 2002.CrossRefGoogle Scholar
  20. 20.
    A. Siepel. An algorithm to find all sorting reversals. In Proc. RECOMB 2002, pages 281–290. ACM Press, 2002.Google Scholar
  21. 21.
    G. Tesler. Efficient algorithms for multichromosomal genome rearrangement. J. Comput. Syst. Sci., 65(3):587–609, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    T. Uno and M. Yagiura. Fast algorithms to enumerate all common intervals of two permutations. Algorithmica, 26(2):290–309, 2000.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Anne Bergeron
    • 1
  • Jens Stoye
    • 2
  1. 1.LaCIMUniversité du Québec à MontréalCanada
  2. 2.Technische FakultätUniversität BielefeldGermany

Personalised recommendations