A basic problem in the area of combinatorial algorithms for genome evolution is to determine the minimum number of large scale evolutionary events (genome rearrangements) that transform a genome into another. The present paper is a contribution to the algorithmic study of genom evolution by translocations which is an area related to pattern recognition. Furthermore, it may be viewed as a contribution to other areas related to pattern recognition like: error estimation, genetic programming, disease diagnosis. In this paper we consider chromosomes as being linear strings that exchange each other prefixes in the translocation process. A new type of translocation distance between a pair of multi-chromosomal genomes is introduced; we examine the complexity of computing this distance in the case of uniform translocation, that is at each step the strings exchange prefixes of the same length. We present an exact polynomial algorithm based on the “greedy” strategy when the target set is a singleton while a 2-approximation algorithm is provided when considering arbitrary target sets. Some open problems are finally formulated.


Genome Rearrangement Polynomial Algorithm Mathematical Linguistics Target String IEEE 36th Annual Symposium 
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.


  1. 1.
    Bafna, V., Pevzner, P.A.: Sorting by transpositions. In: Proceedings of the 6th ACMSIAM Symposium on Discrete Algorithms (1995)Google Scholar
  2. 2.
    Bafna, V., Pevzner, P.A.: Sorting by reversals: genome rearrangements in plant organelles and evolutionary history of X chromosome. Mol. Biol. Evol. 12, 239–246 (1995)Google Scholar
  3. 3.
    Caprara, A.: Sorting by reversal is difficult. In: Proc. of the First Annual International Conference on Computational Molecular Biology (RECOMB 1997), pp. 75–83. ACM, New York (1997)CrossRefGoogle Scholar
  4. 4.
    Copeland, N.G., et al.: A genetic linkage map of the mouse: Current applications and future prospects. Science 262, 57–65 (1993)CrossRefGoogle Scholar
  5. 5.
    Dassow, J., Mitrana, V., Salomaa, A.: Context-free evolutionary grammars and the language of nucleic acids. BioSystems 4, 169–177 (1997)CrossRefGoogle Scholar
  6. 6.
    Dassow, J., Mitrana, V.: Operations and grammars suggested by the genome evolution. Theoretical Computer Science 270(1-2), 701–738 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    McGeoch, D.J.: Molecular evolution of large DNA viruses of eukaryotes. Seminars in Virology 3, 399–408 (1992)Google Scholar
  8. 8.
    Hannenhalli, S., et al.: Algorithms for genome rearrangements: herpesvirus evolution as a test case. In: Proc. of the 3rd International Conference on Bioinformatics and Complex Genome Analysis (1994)Google Scholar
  9. 9.
    Hannehalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversal. J. of the ACM 46(1), 1–27 (1999)CrossRefGoogle Scholar
  10. 10.
    Hannehalli, S., Pevzner, P.A.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proc. of the IEEE 36th Annual Symposium on Foundation of Computer Science, pp. 581–592 (1995)Google Scholar
  11. 11.
    Hannehalli, S.: Polynomial algorithm for computing translocation distance between genomes. In: Galil, Z., Ukkonen, E. (eds.) CPM 1995. LNCS, vol. 937, pp. 162–176. Springer, Heidelberg (1995)Google Scholar
  12. 12.
    Hartl, D.L., Freifelder, D., Snyder, L.A.: Basic Genetics. Jones and Bartlett Publ., Boston (1988)Google Scholar
  13. 13.
    Karlin, S., Mocarski, E.S., Schachtel, G.A.: Molecular evolution of herpesviruses: genomic and protein comparisons. J. of Virology 68, 1886–1902 (1994)Google Scholar
  14. 14.
    Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangements. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds.) CPM 1993. LNCS, vol. 684, pp. 87–105. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  15. 15.
    Kececioglu, J., Sankoff, D.: Efficient bounds for oriented chromosome-inversion distance. In: Crochemore, M., Gusfield, D. (eds.) CPM 1994. LNCS, vol. 807, pp. 307–325. Springer, Heidelberg (1994)Google Scholar
  16. 16.
    Kececioglu, J., Ravi, R.: Of mice and men: Algorithms for evolutionary distances between genomes with translocation. In: Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, pp. 604–613 (1995)Google Scholar
  17. 17.
    Palmer, J.D., Herbon, L.A.: Plant mitochondrial DNA evolves rapidly in structure, but slowly in sequence. Journal of Molecular Evolution 27, 87–97 (1988)CrossRefGoogle Scholar
  18. 18.
    Pevzner, P.A., Waterman, M.S.: Open combinatorial problems in computational molecular biology. In: Proc. of the 3rd Israel Symposium on Theory of Computing and Systems, pp. 158–163. IEEE Computer Computer Society Press, Los Alamitos (1995)CrossRefGoogle Scholar
  19. 19.
    Sankoff, D.: Edit distance 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)Google Scholar
  20. 20.
    Sankoff, D., et al.: Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89, 6575–6579 (1992)CrossRefGoogle Scholar
  21. 21.
    Therman, E., Susman, M.: Human Chromosomes, Structure, Behavior, and Effects. Springer, Heidelberg (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Carlos Martín-Vide
    • 2
  • Victor Mitrana
    • 1
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Research Group in Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain

Personalised recommendations