Tree alignment

In computational phylogenetics, tree alignment is the problem of producing a multiple sequence alignment on a set of sequences over a fixed tree.

Formally, tree alignment is the following optimization problem.

Input: A set $$S$$ of sequences, a phylogenetic tree $$T$$ leaf-labeled by $$S$$ and an edit distance function $$d$$ between sequences,

Output: A labeling of the internal vertices of $$T$$ such that $$\Sigma_{e \in T} d(e)$$ is minimized, where $$d(e)$$ is the edit distance between the endpoints of $$e$$.