A New Tight Upper Bound on the Transposition Distance

  • Anthony Labarre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3692)


We study the problem of computing the minimal number of adjacent, non-intersecting block interchanges required to transform a permutation into the identity permutation. In particular, we use the graph of a permutation to compute that number for a particular class of permutations in linear time and space, and derive a new tight upper bound on the so-called transposition distance.


Circular Permutation Identity Permutation Oriented Cycle Cycle Graph Black Edge 
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.
    Meidanis, J., Setubal, J.: Introduction to Computational Molecular Biology. Brooks-Cole, Pacific Grove (1997)Google Scholar
  2. 2.
    Pevzner, P.A.: Computational molecular biology. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  3. 3.
    Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM J. Discrete Math. 11, 224–240 (1998), (electronic)Google Scholar
  4. 4.
    Elias, I., Hartman, T.: A 1.375 −Approximation Algorithm for Sorting by Transpositions (2005), (submitted)Google Scholar
  5. 5.
    Christie, D.A.: Genome Rearrangement Problems. PhD thesis, University of Glasgow, Scotland (1998)Google Scholar
  6. 6.
    Hartman, T.: A simpler 1.5-approximation algorithm for sorting by transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 156–169. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Guyer, S.A., Heath, L.S., Vergara, J.P.: Subsequence and run heuristics for sorting by transpositions. In: Fourth DIMACS Algorithm Implementation Challenge. Rutgers University (1995)Google Scholar
  8. 8.
    Vergara, J.P.C.: Sorting by Bounded Permutations. PhD thesis, Virginia Polytechnic Institute, Blacksburg, Virginia, USA (1997)Google Scholar
  9. 9.
    Walter, M.E.M.T., Curado, L.R.A.F., Oliveira, A.G.: Working on the problem of sorting by transpositions on genome rearrangements. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 372–383. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Dias, Z., Meidanis, J.: An Alternative Algebraic Formalism for Genome Rearrangements. Comparative Genomics, 213–223 (2000)Google Scholar
  11. 11.
    Dias, Z., Meidanis, J.: Genome Rearrangements Distance by Fusion, Fission, and Transposition is Easy. In: Proceedings of SPIRE 2001 - String Processing and Information Retrieval, Laguna de San Rafael, Chile, pp. 250–253 (2001)Google Scholar
  12. 12.
    Dias, Z., Meidanis, J., Walter, M.E.M.T.: A New Approach for Approximating The Transposition Distance. In: Proceedings of SPIRE 2000 - String Processing and Information Retrieval, La Coruna, Espagne (2000)Google Scholar
  13. 13.
    Eriksson, H., Eriksson, K., Karlander, J., Svensson, L., Wästlund, J.: Sorting a bridge hand. Discrete Mathematics 241, 289–300 (2001); Selected papers in honor of Helge TverbergzbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hultman, A.: Toric Permutations. Master’s thesis, Dept. of Mathematics, KTH, Stockholm, Sweden (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Anthony Labarre
    • 1
  1. 1.Département de Mathématique, Service de Géométrie, Combinatoire et Théorie des GroupesUniversité Libre de BruxellesBruxellesBelgium

Personalised recommendations