Counting trees are binary trees having the
property that a node has a value representing the sum of the child nodes. The
authors extend this concept to the trees that are not necessarily binary, in
which each node apart the interesting source value has a value which is an
aggregation of values of the whole subtree starting from that node. Aggregations
can be arbitrary expressions, that can be computed from partial aggregations,
such as SUM, COUNT, MIN, MAX, but not AVG. In the case of large hierarchical
structures, obtaining grouping query for a group being a subtree, classically
requires a recursive tabular expression, that is consumed by the grouping query.
With aggregation proposed by the authors, the query reduces to reading a single
value. The paper presents example of such an approach, then a sample interface
for Hibernate, an object-relational mapping system, which allows you to easily
define the relevant tables with aggregations and triggers keeping them up to
date. The proposed interfaces retain Hibernate standards making the solution
transparent for the programmer.
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