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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.

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  • $\begingroup$ 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? $\endgroup$ – Hendrik Jan Mar 5 '17 at 1:52

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