Generalized tree alignment

In computational phylogenetics, generalized tree alignment is the problem of producing a multiple sequence alignment and a phylogenetic tree on a set of sequences simultaneously, as opposed to separately.

Formally, Generalized tree alignment is the following optimization problem.

Input: A set $$S$$ and an edit distance function $$d$$ between sequences,

Output: A tree $$T$$ leaf-labeled by $$S$$ and labeled with sequences at the internal nodes, such that $$\Sigma_{e \in T} d(e)$$ is minimized, where $$d(e)$$ is the edit distance between the endpoints of $$e$$.

Note that this is in contrast to tree alignment, where the tree is provided as input.