Approximation Algorithms for Multiple Sequence Alignment Under a Fixed Evolutionary Tree

We consider the problem of aligning sequences related by a given evolutionary tree: given a fixed tree with its leaves labeled with sequences, find ancestral sequences to label the internal nodes so as to minimize the total cost of all the edges in the tree. The cost of an edge is the edit distance between the sequences labeling its endpoints. In this paper, we consider the case when the given tree is a regular d-ary tree for some fixed d and provide a d+1/d−1-approximation algorithm for this problem that runs in time O(d(2kn) d + n2k2d) where k is the number of leaves in the tree and n is the maximum length of any of the sequences labeling the leaves.

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