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.
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References
Apostolico, A., Atallah, M., Larmore, L., McFaddin, S.: Efficient parallel algorithms for string editing problems. SIAM J. Comput. 19, 968–998 (1990)
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)
Benson, G.: A space efficient algorithm for finding the best nonoverlapping alignment score. Theoretical Computer Science 145, 357–369 (1995)
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)
Gelfand, M.S., Mironov, A.A., Pevzner, P.A.: Gene Recognition Via Spliced Sequence Alignment. Proc. Natl. Acad. Sci. USA 93, 9061–9066 (1996)
Hanan, M.: On Steiner’s problem with rectiliniar distance. SIAM J. Appl. Match. 14, 255–265 (1966)
Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem, Annals of Discrete Mathematics. North-Holland Publisher, Amsterdam (1992)
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)
Kim, S., Park, K.: A Dynamic Edit Distance Table. J. Discrete Algorithms 2(2), 303–312 (2004)
Landau, G.M., Myers, E.W., Schmidt, J.P.: Incremental String Comparison. SIAM J. Comput. 27(2), 557–582 (1998)
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)
Landau, G.M., Ziv-Ukelson, M.: On the Common Substring Alignment Problem. Journal of Algorithms 41(2), 338–359 (2001)
Lu, B., Ruan, L.: Polynomial Time Approximation Scheme for the Rectilinear Steiner Arborescence Problem. Journal of Combinatorial Optimization 4 (3), 357–363 (2000)
Ladeira de Matos, R.R.: A Rectilinear Arborescence Problem, Dissertation, University of Alabama (1979)
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)
Monge, G., et Remblai, D.: Mémoires de l’Academie des Sciences, Paris (1781)
Masek, W.J., Paterson, M.S.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20, 18–31 (1980)
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)
Rao, S.K., Sadayappan, P., Hwang, F.K., Shor, P.W.: The rectilinear Steiner arborescence problem. Algorithmica 7, 277–288 (1992)
Roytberg, M.A., Astakhova, T.V., Gelfand, M.S.: Combinatorial Approaches to Gene Recognition. Computers Chemistry 21(4), 229–235 (1997)
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)
Ukkonen, E.: Finding Approximate Patterns in Strings. J. Algorithms 6, 132–137 (1985)
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Kent, C., Landau, G.M., Ziv-Ukelson, M. (2005). On the Complexity of Sparse Exon Assembly. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_18
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DOI: https://doi.org/10.1007/11496656_18
Publisher Name: Springer, Berlin, Heidelberg
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