Paths and Cycles in Breakpoint Graphs of Random Multichromosomal Genomes

  • Wei Xu
  • Chunfang Zheng
  • David Sankoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4205)


We study the probability distribution of genomic distance d under the hypothesis of random gene order. We interpret the random order assumption in terms of a stochastic method for constructing the alternating colour cycles in the decomposition of the bicoloured breakpoint graph. For two random genomes of length n and χ chromosomes, we show that the expectation of n + χd is \(O(\frac{1}{2}\log\frac{n+\chi}{2\chi}+\frac{3}{2}\chi)\). We then discuss how to extend these analyses to the case where intra- and interchromosomal operations have different probabilities.


Syntenic Block Genomic Distance Linear Chromosome Black Edge Breakpoint Graph 
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.
    Eriksen, N., Hultman, A.: Estimating the expected reversal distance after a fixed number of reversals. Advances of Applied Mathematics 32, 439–453 (2004)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kim, J.H., Wormald, N.C.: Random matchings which induce Hamilton cycles, and Hamiltonian decompositions of random regular graphs. Journal of Combinatorial Theory, Series B 81, 20–44 (2001)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Mazowita, M., Haque, L., Sankoff, D.: Stability of rearrangement measures in the comparison of genome sequences. Journal of Computational Biology 13, 554–566 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Sankoff, D.: The signal in the genomes. PLoS Computational Biology 2, 35 (2006)CrossRefGoogle Scholar
  5. 5.
    Sankoff, D., Haque, L.: The distribution of genomic distance between random genomes. Journal of Computational Biology 13, 1005–1012 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Tesler, G.: Efficient algorithms for multichromosomal genome rearrangements. Journal of Computer and System Sciences 65, 587–609 (2002)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21, 3340–3346 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wei Xu
    • 1
  • Chunfang Zheng
    • 2
  • David Sankoff
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaCanada
  2. 2.Department of BiologyUniversity of OttawaCanada

Personalised recommendations