  The largest common embeddable subtree problem asks for the largest possible
tree embeddable into two input trees and generalizes the classical maximum
common subtree problem. Several variants of the problem in labeled and
unlabeled rooted trees have been studied, e.g., for the comparison of
evolutionary trees. We consider a generalization, where the sought embedding is
maximal with regard to a weight function on pairs of labels. We support rooted
and unrooted trees with vertex and edge labels as well as distance penalties
for skipping vertices. This variant is important for many applications such as
the comparison of chemical structures and evolutionary trees. Our algorithm
computes the solution from a series of bipartite matching instances, which are
solved efficiently by exploiting their structural relation and imbalance. Our
analysis shows that our approach improves or matches the running time of the
formally best algorithms for several problem variants. Specifically, we obtain
a running time of $\mathcal O(|T|\,|T'|\Delta)$ for two rooted or unrooted
trees $T$ and $T'$, where $\Delta=\min\{\Delta(T),\Delta(T')\}$ with
$\Delta(X)$ the maximum degree of $X$. If the weights are integral and at most
$C$, we obtain a running time of $\mathcal O(|T|\,|T'|\sqrt\Delta\log
(C\min\{|T|,|T'|\}))$ for rooted trees.
