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On the Complexity of Sparse Exon Assembly

  • Carmel Kent
  • Gad M. Landau
  • Michal Ziv-Ukelson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3537)

Abstract

Gene structure prediction is one of the most important problems in computational molecular biology. A combinatorial approach to the problem, denoted Gene Prediction via Spliced Alignment, was introduced by Gelfand, Mironov and Pevzner [5]. The method works by finding a set of blocks in a source genomic sequence S whose concatenation (splicing) fits a target gene T belonging to a homologous species. Let S,T and the candidate exons be sequences of size O(n). The innovative algorithm described in [5] yields an O(n 3) result for spliced alignment, regardless of filtration mode.

In this paper we suggest a new algorithm which targets the case where filtering has been applied to the data, resulting in a set of O(n) candidate exon blocks. Our algorithm yields an \(O(n^2 \sqrt{n})\) solution for this case.

Keywords

Edit Distance Steiner Point Grid Graph Linear Encode Space Complexity Analysis 
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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References

  1. 1.
    Apostolico, A., Atallah, M., Larmore, L., McFaddin, S.: Efficient parallel algorithms for string editing problems. SIAM J. Comput. 19, 968–998 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aggarawal, A., Park, J.: Notes on Searching in Multidimensional Monotone Arrays. In: Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 497–512 (1988)Google Scholar
  3. 3.
    Benson, G.: A space efficient algorithm for finding the best nonoverlapping alignment score. Theoretical Computer Science 145, 357–369 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Crochemore, M., Landau, G.M., Schieber, B., Ziv-Ukelson, M.: Re-Use Dynamic Programming for Sequence Alignment: An Algorithmic Toolkit, String Algorithmices. NATO Book series. KCL Press (2004)Google Scholar
  5. 5.
    Gelfand, M.S., Mironov, A.A., Pevzner, P.A.: Gene Recognition Via Spliced Sequence Alignment. Proc. Natl. Acad. Sci. USA 93, 9061–9066 (1996)CrossRefGoogle Scholar
  6. 6.
    Hanan, M.: On Steiner’s problem with rectiliniar distance. SIAM J. Appl. Match. 14, 255–265 (1966)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem, Annals of Discrete Mathematics. North-Holland Publisher, Amsterdam (1992)Google Scholar
  8. 8.
    Kannan, S.K., Myers, E.W.: An Algorithm For Locating Non-Overlapping Regions of Maximum Alignment Score. SIAM J. Comput. 25(3), 648–662 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kim, S., Park, K.: A Dynamic Edit Distance Table. J. Discrete Algorithms 2(2), 303–312 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Landau, G.M., Myers, E.W., Schmidt, J.P.: Incremental String Comparison. SIAM J. Comput. 27(2), 557–582 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Landau, G.M., Myers, E.W., Ziv-Ukelson, M.: Two Algorithms for LCS Consecutive Suffix Alignment. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 173–193. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Landau, G.M., Ziv-Ukelson, M.: On the Common Substring Alignment Problem. Journal of Algorithms 41(2), 338–359 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lu, B., Ruan, L.: Polynomial Time Approximation Scheme for the Rectilinear Steiner Arborescence Problem. Journal of Combinatorial Optimization 4 (3), 357–363 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ladeira de Matos, R.R.: A Rectilinear Arborescence Problem, Dissertation, University of Alabama (1979)Google Scholar
  15. 15.
    Mironov, A.A., Roytberg, M.A., Pevzner, P.A., Gelfand, M.S.: Performance- Guarantee Gene Predictions Via Spliced Alignemnt. Genomics 51 A.N. GE985251, 332–339 (1998)Google Scholar
  16. 16.
    Monge, G., et Remblai, D.: Mémoires de l’Academie des Sciences, Paris (1781)Google Scholar
  17. 17.
    Masek, W.J., Paterson, M.S.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20, 18–31 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Schmidt, J.P.: All Highest Scoring Paths In Weighted Grid Graphs and Their Application To Finding All Approximate Repeats In Strings. SIAM J. Comput. 27(4), 972–992 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Rao, S.K., Sadayappan, P., Hwang, F.K., Shor, P.W.: The rectilinear Steiner arborescence problem. Algorithmica 7, 277–288 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Roytberg, M.A., Astakhova, T.V., Gelfand, M.S.: Combinatorial Approaches to Gene Recognition. Computers Chemistry 21(4), 229–235 (1997)CrossRefGoogle Scholar
  21. 21.
    Sze, S.-H., Pevzner, P.A.: Las Vegas Algorithms for Gene Recognition: Suboptimal and Error-Tolerant Spliced Alignment. J. Comp. Biol. 4(3), 297–309 (1997)CrossRefGoogle Scholar
  22. 22.
    Ukkonen, E.: Finding Approximate Patterns in Strings. J. Algorithms 6, 132–137 (1985)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Carmel Kent
    • 1
  • Gad M. Landau
    • 1
    • 2
  • Michal Ziv-Ukelson
    • 3
  1. 1.Dept. of Computer ScienceHaifa UniversityHaifaIsrael
  2. 2.Department of Computer and Information SciencePolytechnic UniversityBrooklynUSA
  3. 3.Dept. of Computer ScienceTechnion – Israel Institute of TechnologyHaifaIsrael

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