Upward accumulation refers to accumulating on each node information about all decedents. Downward accumulation refers to accumulating on each node information of every ancestor.
One application would be calculating national election results. Construct a tree with the root node as the entire nation and each level representing refined geographical areas such as states/provinces, counties/parishes, cities/townships, and polling districts as the leaves. By accumulating the vote totals from the polling districts, one can compute the vote totals for each of the larger geographic areas.
Gibbons et al. formally define binary tree accumulation as iterative application of a ternary operator ; where A are descendant labels and B is a junction label.
- Gibbons, Jeremy (1991). Algebras for Tree Algorithms (PDF) (Ph.D.). Oxford University.
- Gibbons, Jeremy; Cai, Wentong; Skillcorn, David B. (1994). "Efficient parallel algorithms for tree accumulations". Science of Computer Programming. Elsiver.