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HMM, GA, SA methods |
m →Dynamic programming and computational complexity: not just NP-hard, it's NP-complete |
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The most direct method for producing an MSA uses the [[dynamic programming]] technique to identify the globally optimal alignment solution. For proteins, this method usually involves two sets of parameters: a [[gap penalty]] and a [[substitution matrix]] assigning scores or probabilities to the alignment of each possible pair of amino acids based on the similarity of the amino acids' chemical properties and the evolutionary probability of the mutation. For nucleotide sequences a substitution matrix can be used, but since there are only four possible standard characters per sequence and the individual nucleotides do not typically differ much in substitution probability, the parameters for DNA and RNA sequences usually consist of a gap penalty, a positive score for character matches, and a negative score for mismatches.
For ''n'' individual sequences, the method requires constructing the ''n''-dimensional equivalent of the matrix formed in standard pairwise dynamic programming. The search space thus increases exponentially with increasing ''n'' and is also strongly dependent on sequence length. To find the global optimum for ''n'' sequences this way has been shown to be an [[NP-
==Progressive alignment construction==
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