Abstract
Multiple sequence alignment is a task at the heart of much of current computational biology [4]. Several different objective functions have been proposed to formalize the task of multiple sequence alignment, but efficient algorithms are lacking in each case. Thus multiple sequence alignment is one of the most critical, essentially unsolved problems in computational biology. In this paper we consider one of the more compelling objective functions for multiple sequence alignment, formalized as the tree alignment problem. Previously in [15], a factor-of-two approximation method was developed for tree alignment, which ran in cubic time (as a function of the number of fixed length strings to be aligned), along with a polynomial time approximation scheme (PTAS) for the problem. However, the PTAS in [15] had a running time which made it impractical to reduce the error bound much below two for small size biological sequences (100 characters long).
In this paper we first develop a factor-of-two approximation algorithm which runs in quadratic time, and then use it to develop a PTAS which has a smaller guaranteed error bound and a vastly improved worst case running time compared to the scheme in [15]. With the new approximation scheme, it is now practical to guarantee an error bound of 1.583 for strings of lengths 200 characters or less.
Partially supported by Dept. of Energy grant DE-FG03-90ER60999.
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S. Altschul and D. Lipman, Trees, stars, and multiple sequence alignment, SIAM Journal on Applied Math. 49, pp. 197–209, 1989
S. C. Chan, A. K. C. Wong and D. K. T. Chiu, A survey of multiple sequence comparison methods, Bulletin of Mathematical Biology 54(4), pp. 563–598, 1992.
S.K. Gupta, J. D. Kececioglu, and A. A. Schaffer, Making the shortest-paths approach to sum-of-pairs multiple sequence alignment more space efficient in practice, CPM95, pp. 128–143.
D. Gusfield, Efficient methods for multiple sequence alignment with guaranteed error bounds, Bulletin of Mathematical Biology 55, pp. 141–154, 1993.
J. J. Hein, A new method that simultaneously aligns and reconstructs ancestral sequences for any number of homologous sequences, when the phylogeny is given, Mol. Biol. Evol. 6(6), pp. 649–668, 1989.
D. J. Lipman, S. F. Altschul, and J. D. Kececioglu, A tool for multiple sequence alignment. Proc. Natl. Acad. Sci. USA., 86:4412–4415, 1989.
R. Ravi and J. Kececioglu, Approximation algorithms for multiple sequence alignment under a fixed evolutionary tree, CPM95, pp. 330–339.
D. Sankoff, Minimal mutation trees of sequences, SIAM J. Applied Math. 28(1), pp. 35–42, 1975.
D. Sankoff, R. J. Cedergren and G. Lapalme, Frequency of insertion-deletion, transversion, and transition in the evolution of 5S ribosomal RNA, J. Mol. Evol. 7, pp. 133–149, 1976.
D. Sankoff and R. Cedergren, Simultaneous comparisons of three or more sequences related by a tree, In D. Sankoff and J. Kruskal, editors, Time warps, string edits, and macromolecules: the theory and practice of sequence comparison, pp. 253–264, Addison Wesley, 1983.
D. Sankoff and J. Kruskal, Time warps, string edits, and macromolecules: the theory and practice of sequence comparison, Addison Wesley, 1983
R. Ravi and J. kececioglu, Approximation algorithms for multiple sequence alignment under a fixed evolutionary tree, CPM95, pp. 330–339.
M.S. Waterman and M.D. Perlwitz, Line geometries for sequence comparisons”, Bull. Math. Biol. 46, pp. 567–577, 1984.
L. Wang and T. Jiang, On the complexity of multiple sequence alignment, Journal of Computational Biology, vol. 1, pp. 337–348, 1994.
L.Wang, T. Jiang, and E.L. Lawler, Aligning sequences via an evolutionary tree: complexity and approximation, Algorithmica, to appear; also presented at the 26th ACM Symp. on Theory of Computing, 1994.
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© 1996 Springer-Verlag Berlin Heidelberg
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Wang, L., Gusfield, D. (1996). Improved approximation algorithms for tree alignment. In: Hirschberg, D., Myers, G. (eds) Combinatorial Pattern Matching. CPM 1996. Lecture Notes in Computer Science, vol 1075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61258-0_17
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DOI: https://doi.org/10.1007/3-540-61258-0_17
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