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.^[1]

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 ${\displaystyle \Sigma _{e\in T}d(e)}$ is minimized, where ${\displaystyle d(e)}$ is the edit distance between the endpoints of $e$.^[2]

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

References

1. Schwikowski, Benno; Vingron, Martin (1997). "The Deferred Path Heuristic for the Generalized Tree Alignment Problem". Journal of Computational Biology. 4 (3): 415–431. doi:10.1089/cmb.1997.4.415. ISSN 1066-5277.
2. Srinivas Aluru (21 December 2005). Handbook of Computational Molecular Biology. CRC Press. pp. 19–26. ISBN 978-1-4200-3627-5.