Tree alignment
Encyclopedia
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
of sequences, a phylogenetic tree
leaf-labeled by 
and an edit distance
function
between sequences,
Output: A labeling of the internal vertices of
such that 
is minimized, where 
is the edit distance
between the endpoints of
.
The task is NP-hard
Multiple sequence alignment
A multiple sequence alignment is a sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evolutionary relationship by which they share a lineage and are descended from a common ancestor...
on a set of sequences over a fixed tree.
Formally, tree alignment is the following optimization problem.
Input: A set
of sequences, a phylogenetic treePhylogenetic tree
A phylogenetic tree or evolutionary tree is a branching diagram or "tree" showing the inferred evolutionary relationships among various biological species or other entities based upon similarities and differences in their physical and/or genetic characteristics...
leaf-labeled by and an edit distanceEdit distance
In information theory and computer science, the edit distance between two strings of characters generally refers to the Levenshtein distance. However, according to Nico Jacobs, “The term ‘edit distance’ is sometimes used to refer to the distance in which insertions and deletions have equal cost and...
function
between sequences,Output: A labeling of the internal vertices of
such that is minimized, where is the edit distanceEdit distance
In information theory and computer science, the edit distance between two strings of characters generally refers to the Levenshtein distance. However, according to Nico Jacobs, “The term ‘edit distance’ is sometimes used to refer to the distance in which insertions and deletions have equal cost and...
between the endpoints of
.The task is NP-hard
NP-hard
NP-hard , in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H...