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 Σ e ∈ 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.