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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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 118; no. 3; pp. 181 - 198
Main Authors: Fernández-Baca, David, Seppäläinen, Timo, Slutzki, Giora
Format: Journal Article
Language:English
Published: Lausanne Elsevier B.V 15.05.2002
Amsterdam Elsevier
New York, NY
Subjects:
Computational biology
Exact sciences and technology
Experimental analysis of algorithms
Mathematics
Multiple alignment
Parametric analysis
Sciences and techniques of general use
Sequence alignment
Parametric analysis
Experimental analysis of algorithms
Multiple alignment
Sequence alignment
Computational biology
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(01)00206-2