## Three Sequences

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Aligning three sequences is an important special case of multiple alignment. Each internal node in an unrooted phylogenetic (evolutionary) tree has three neighbours, so iterated three-way alignment is a practical way to infer hypothetical ancestral sequences given a number of descendant (leaf) sequences.

If the costs are "simple" {0,1} it is possible [Allison] to write a fast [algorithm] for this problem, one that runs in O(n+d3)-time on average where n is the average length of the sequences and d is the 3-way edit distance. If the sequences are similar, d << n.

This technique can be extended [Powell et al (ii)] to linear gap costs (affine) with "small" integer costs.

Divide and conquer [Powell et al (i)] can be used to reduce the amount of space used to O(d2) even when an optimal alignment is required.

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