Bounds for parametric sequence comparison
We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight 3(n/2π) 2/3+O(n 1/3 log n) bound on the worst-case number of distinct optimum alignments for two sequences of length n as the parameters are varied....
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| Vydané v: | Discrete Applied Mathematics Ročník 118; číslo 3; s. 181 - 198 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Lausanne
Elsevier B.V
15.05.2002
Amsterdam Elsevier New York, NY |
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight
3(n/2π)
2/3+O(n
1/3
log
n)
bound on the worst-case number of distinct optimum alignments for two sequences of length
n as the parameters are varied. This refines a
O(
n
2/3) upper bound by Gusfield et al., answering a question posed by Pevzner and Waterman. Our lower bound requires an unbounded alphabet. For strings over a binary alphabet, we prove a
Ω(n
1/2)
lower bound. For the parametric global alignment of
k⩾2 sequences under sum-of-pairs scoring we prove a
3((
k
2
)n/2π)
2/3+O(k
2/3n
1/3
log
n)
upper bound on the number of distinct optimality regions and a
Ω(n
2/3)
lower bound, partially answering a problem of Pevzner. Based on experimental evidence, we conjecture that for two random sequences, the number of optimality regions is approximately
n
with high probability. |
|---|---|
| AbstractList | We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight
3(n/2π)
2/3+O(n
1/3
log
n)
bound on the worst-case number of distinct optimum alignments for two sequences of length
n as the parameters are varied. This refines a
O(
n
2/3) upper bound by Gusfield et al., answering a question posed by Pevzner and Waterman. Our lower bound requires an unbounded alphabet. For strings over a binary alphabet, we prove a
Ω(n
1/2)
lower bound. For the parametric global alignment of
k⩾2 sequences under sum-of-pairs scoring we prove a
3((
k
2
)n/2π)
2/3+O(k
2/3n
1/3
log
n)
upper bound on the number of distinct optimality regions and a
Ω(n
2/3)
lower bound, partially answering a problem of Pevzner. Based on experimental evidence, we conjecture that for two random sequences, the number of optimality regions is approximately
n
with high probability. |
| Author | Fernández-Baca, David Slutzki, Giora Seppäläinen, Timo |
| Author_xml | – sequence: 1 givenname: David surname: Fernández-Baca fullname: Fernández-Baca, David email: fernande@cs.iastate.edu organization: Department of Computer Science, Iowa State University, 226 Atanasoff Hall, Ames, IA 50011, USA – sequence: 2 givenname: Timo surname: Seppäläinen fullname: Seppäläinen, Timo email: seppalai@iastate.edu organization: Department of Mathematics, Iowa State University, Ames, IA 50011, USA – sequence: 3 givenname: Giora surname: Slutzki fullname: Slutzki, Giora email: slutzki@cs.iastate.edu organization: Department of Computer Science, Iowa State University, 226 Atanasoff Hall, Ames, IA 50011, USA |
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| Issue | 3 |
| Keywords | Parametric analysis Experimental analysis of algorithms Multiple alignment Sequence alignment Computational biology |
| Language | English |
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| References | Pevzner (BIB8) 2000 Gusfield (BIB4) 1997 Waterman, Eggert, Lander (BIB12) 1992; 89 Carrillo, Lipman (BIB2) 1988; 48 Gusfield, Balasubramanian, Naor (BIB5) 1994; 12 D. Gusfield, P. Stelling, Parametric and inverse-parametric sequence alignment with XPARAL, in:Russell F. Doolittle (Eds.), Computer Methods for Macromolecular Sequence Analysis, Methods in Enzymology, Vol. 266, Academic Press, New York, 1996, 481–494. Fernández-Baca, Seppäläinen, Slutzki (BIB3) 2000; Vol. 1848 Sankoff, Kruskal (Eds.) (BIB10) 1983 P.A. Pevzner, M.S. Waterman, Open combinatorial problems in computational molecular biology, Proceedings of the Third Israeli Symposium on Theory of Computing and Systems, IEEE Computer Society Press, Silver Spring, MD, 1995, 158–173. Huang, Pevzner, Miller (BIB7) 1994; Vol. 807 Vingron, Waterman (BIB11) 1994; 235 Apostol (BIB1) 1976 Gusfield (10.1016/S0166-218X(01)00206-2_BIB4) 1997 Pevzner (10.1016/S0166-218X(01)00206-2_BIB8) 2000 Fernández-Baca (10.1016/S0166-218X(01)00206-2_BIB3) 2000; Vol. 1848 Gusfield (10.1016/S0166-218X(01)00206-2_BIB5) 1994; 12 Sankoff (10.1016/S0166-218X(01)00206-2_BIB10) 1983 Huang (10.1016/S0166-218X(01)00206-2_BIB7) 1994; Vol. 807 Apostol (10.1016/S0166-218X(01)00206-2_BIB1) 1976 10.1016/S0166-218X(01)00206-2_BIB6 Waterman (10.1016/S0166-218X(01)00206-2_BIB12) 1992; 89 Carrillo (10.1016/S0166-218X(01)00206-2_BIB2) 1988; 48 Vingron (10.1016/S0166-218X(01)00206-2_BIB11) 1994; 235 10.1016/S0166-218X(01)00206-2_BIB9 |
| References_xml | – year: 1976 ident: BIB1 publication-title: Introduction to Analytic Number Theory – volume: Vol. 1848 start-page: 69 year: 2000 end-page: 83 ident: BIB3 article-title: Parametric multiple sequence alignment and phylogeny construction publication-title: Combinatorial Pattern Matching – year: 2000 ident: BIB8 publication-title: Computational Molecular Biology – volume: 48 start-page: 1073 year: 1988 end-page: 1082 ident: BIB2 article-title: The multiple sequence alignment problem in biology publication-title: SIAM J. Appl. Math. – year: 1997 ident: BIB4 publication-title: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology – volume: Vol. 807 start-page: 87 year: 1994 end-page: 101 ident: BIB7 article-title: Parametric recomputing in alignment graphs publication-title: Combinatorial Pattern Matching – volume: 12 start-page: 312 year: 1994 end-page: 326 ident: BIB5 article-title: Parametric optimization of sequence alignment publication-title: Algorithmica – volume: 235 start-page: 1 year: 1994 end-page: 12 ident: BIB11 article-title: Sequence alignment and penalty choice: review of concepts, case studies, and implications publication-title: J. Mol. Biol. – reference: D. Gusfield, P. Stelling, Parametric and inverse-parametric sequence alignment with XPARAL, in:Russell F. Doolittle (Eds.), Computer Methods for Macromolecular Sequence Analysis, Methods in Enzymology, Vol. 266, Academic Press, New York, 1996, 481–494. – year: 1983 ident: BIB10 publication-title: Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison – volume: 89 start-page: 6090 year: 1992 end-page: 6093 ident: BIB12 article-title: Parametric sequence comparisons publication-title: Proc. Natl. Acad. Sci. USA – reference: P.A. Pevzner, M.S. Waterman, Open combinatorial problems in computational molecular biology, Proceedings of the Third Israeli Symposium on Theory of Computing and Systems, IEEE Computer Society Press, Silver Spring, MD, 1995, 158–173. – volume: Vol. 1848 start-page: 69 year: 2000 ident: 10.1016/S0166-218X(01)00206-2_BIB3 article-title: Parametric multiple sequence alignment and phylogeny construction – volume: Vol. 807 start-page: 87 year: 1994 ident: 10.1016/S0166-218X(01)00206-2_BIB7 article-title: Parametric recomputing in alignment graphs – volume: 12 start-page: 312 year: 1994 ident: 10.1016/S0166-218X(01)00206-2_BIB5 article-title: Parametric optimization of sequence alignment publication-title: Algorithmica doi: 10.1007/BF01185430 – ident: 10.1016/S0166-218X(01)00206-2_BIB6 doi: 10.1016/S0076-6879(96)66030-3 – year: 2000 ident: 10.1016/S0166-218X(01)00206-2_BIB8 – year: 1976 ident: 10.1016/S0166-218X(01)00206-2_BIB1 – volume: 89 start-page: 6090 year: 1992 ident: 10.1016/S0166-218X(01)00206-2_BIB12 article-title: Parametric sequence comparisons publication-title: Proc. Natl. Acad. Sci. USA doi: 10.1073/pnas.89.13.6090 – year: 1983 ident: 10.1016/S0166-218X(01)00206-2_BIB10 – volume: 235 start-page: 1 year: 1994 ident: 10.1016/S0166-218X(01)00206-2_BIB11 article-title: Sequence alignment and penalty choice: review of concepts, case studies, and implications publication-title: J. Mol. Biol. doi: 10.1016/S0022-2836(05)80006-3 – year: 1997 ident: 10.1016/S0166-218X(01)00206-2_BIB4 – volume: 48 start-page: 1073 year: 1988 ident: 10.1016/S0166-218X(01)00206-2_BIB2 article-title: The multiple sequence alignment problem in biology publication-title: SIAM J. Appl. Math. doi: 10.1137/0148063 – ident: 10.1016/S0166-218X(01)00206-2_BIB9 doi: 10.1109/ISTCS.1995.377035 |
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| Snippet | We consider the problem of computing a global alignment between two or more sequences subject to varying mismatch and indel penalties. We prove a tight
3(n/2π)... |
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| SubjectTerms | Computational biology Exact sciences and technology Experimental analysis of algorithms Mathematics Multiple alignment Parametric analysis Sciences and techniques of general use Sequence alignment |
| Title | Bounds for parametric sequence comparison |
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