# a variant of Fitch's algorithm when it is known that one path has cost 0?

Fitch's algorithm solves the small parsimony problem - given tree topology and leaf labels, but not internal node labels, find best internal node labels (i.e. best score) for that tree. The score is the number of edges $u->v$ with different labels $L_u \neq L_v$.

I need a variant on Fitch's algorithm when it is known that there is one path from root to some leaf with cost 0.

• Fitch will give you a set of labels for each node. If your assumption is right there must be a leaf with label such that all nodes on the path from the leaf to the root carry that label. Can't you just find such a label and assign that to the root? – Hendrik Jan Mar 5 '17 at 1:52