Quadratic Time Algorithms for Finding Common Intervals in Two and More Sequences

  • Thomas Schmidt
  • Jens Stoye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3109)


A popular approach in comparative genomics is to locate groups or clusters of orthologous genes in multiple genomes and to postulate functional association between the genes contained in such clusters. To this end, genomes are often represented as permutations of their genes, and common intervals, i.e. intervals containing the same set of genes, are interpreted as gene clusters. A disadvantage of modelling genomes as permutations is that paralogous copies of the same gene inside one genome can not be modelled.

In this paper we consider a slightly modified model that allows paralogs, simply by representing genomes as sequences rather than permutations of genes. We define common intervals based on this model, and we present a simple algorithm that finds all common intervals of two sequences in Θ(n 2) time using Θ(n 2) space. Another, more complicated algorithm runs in O(n 2) time and uses only linear space. We also show how to extend the simple algorithm to more than two genomes, and we present results from the application of our algorithms to real data.


Gene Cluster Paralogous Gene Maximal Interval Common Interval Paralogous Copy 
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.
    Amir, A., Apostolico, A., Landau, G.M., Satta, G.: Efficient text fingerprinting via parikh mapping. J. Discr. Alg. 26, 1–13 (2003)MathSciNetGoogle Scholar
  2. 2.
    Bender, M.A., Farach-Colton, M.: The LCA problem revisited. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 88–94. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bork, P., Snel, B., Lehmann, G., Suyama, M., Dandekar, T., Lathe III, W., Huynen, M.A.: Comparative genome analysis: exploiting the context of genes to infer evolution and predict function. In: Sankoff, D., Nadeau, J.H. (eds.) Comparative genomics, pp. 281–294. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  4. 4.
    Didier, G.: Common intervals of two sequences. In: Benson, G., Page, R.D.M. (eds.) WABI 2003. LNCS (LNBI), vol. 2812, pp. 17–24. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Durand, D., Sankoff, D.: Tests for gene clustering. J. Comput. Biol. 10(3/4), 453–482 (2002)Google Scholar
  6. 6.
    Heber, S., Stoye, J.: Finding all common intervals of k permutations. In: Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching, CPM 2001, pp. 207–218 (2001)Google Scholar
  7. 7.
    Lathe III, W.C., Snel, B., Bork, P.: Gene context conservation of a higher order than operons. Trends Biochem. Sci. 25, 474–479 (2000)CrossRefGoogle Scholar
  8. 8.
    Overbeek, R., Fonstein, M., D’Souza, M., Pusch, G.D., Maltsev, N.: The use of gene clusters to infer functional coupling. Proc. Natl. Acad. Sci. USA 96, 2896–2901 (1999)CrossRefGoogle Scholar
  9. 9.
    Rogozin, I.B., Makarova, K.S., Murvai, J., Czabarka, E., Wolf, Y.I., Tatusov, R.L., Szekely, L.A., Koonin, E.V.: Connected gene neighborhoods in prokaryotic genomes. Nucleic Acids Res 30, 2212–2223 (2002)CrossRefGoogle Scholar
  10. 10.
    Tamames, J., Casari, G., Ouzounis, C., Valencia, A.: Conserved clusters of functionally related genes in two bacterial genomes. J. Mol. Evol. 44, 66–73 (1997)CrossRefGoogle Scholar
  11. 11.
    Tatusov, R.L., Natale, D.A., Garkavtsev, I.V., Tatusova, T.A., Shankavaram, U.T., Rao, B.S., Kiryutin, B., Galperin, M.Y., Fedorova, N.D., Koonin, E.V.: The COG database: new developments in phylogenetic classification of proteins from complete genomes. Nucleic Acids Res 29, 22–28 (2001)CrossRefGoogle Scholar
  12. 12.
    Uno, T., Yagiura, M.: Fast algorithms to enumerate all common intervals of two permutations. Algorithmica 26, 290–309 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Yanai, I., DeLisi, C.: The society of genes: networks of functional links between genes from comparative genomics. Genome Biol. 3(0064), 1–12 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thomas Schmidt
    • 1
  • Jens Stoye
    • 2
  1. 1.International NRW Graduate School in Bioinformatics and Genome Research, Center of BiotechnologyUniversität BielefeldBielefeldGermany
  2. 2.Technische FakultätUniversität BielefeldBielefeldGermany

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