A subtree query asks for the heaviest in a subtree which is specified by
providing two vertices $v$ and $r$; $r$ is the root of the tree and $v$ is
root of the subtree. To support subtree queries, we tag the cluster with
the heaviest edge in that subtree. It is easy to specify the rake,
compress, and finalize operations for this purpose. To find the heaviest
edge in a given subtree, we start at $v$ and $r$ and walk up the RC-Tree
until they meet. For the tree-root $r$, we maintain no information, for
the subtree-root $v$, we maintain the heaviest edge in the subtree rooted
at $v$ with respect to each boundary vertex as the root. When the two
paths meet, we compute the answer by taking the maximum of cluster for $r$
and the value for the common boundary vertex.