  Binary Partition Hierarchies (BPH) and minimum spanning trees are fundamental
data structures involved in hierarchical analysis such as quasi-flat zones or
watershed. However, classical BPH construction algorithms require to have the
whole data in memory, which prevent the processing of large images that cannot
fit entirely in the main memory of the computer. To cope with this problem, an
algebraic framework leading to a high level calculus was introduced allowing an
out-of-core computation of BPHs. This calculus relies on three operations:
select, join, and insert. In this article, we introduce three efficient
algorithms to perform these operations providing pseudo-code and complexity
analysis.
