Tree accumulation
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In Computer Science, tree accumulation is the process of accumulating data placed in tree nodes according to their tree structure. Formally this operation is a catamorphism.
Upward accumulation refers to accumulating on each node information about all decedents. Downward accumulation refers to accumulating on each node information of every ancestor.
Gibbons, Jeremy (1991). Algebras for Tree Algorithms (PDF) (Ph.D.). Oxford University.