To support path queries, we will annotate each binary
cluster in the RC-Tree with the weight of the maximum edge on the
path between its two boundary vertices; for future reference call this
path the {\em cluster path}. All other cluster (unary and nullary) will
have no tags. This requires that the user specify \rakeData, and
\finalizeData to be ``no-ops'', and define \compressData to be the maximum
operation on edge weights. By using the annotations, the user then writes
a function that finds the maximum edge weight on a given path as follows.
Let $u$ and $v$ be the two ends of the path. Starting at $u$ and $v$ in
the RC-Tree and walk up the RC-Trees while maintaining the weight of the
heaviest edge on the path from $u$ and $v$ to the endpoints of the
clusters that they are included. When the two clusters meet, the maximum
of the two weights corresponding to the common end-point will yield the
result.