The \operatorname{compose} operator as defined above actually captures a ton of things:

- Chunking is the composition of a single linearization.
~~Pure ancestor sort is the composition of all ancestor sets in a cluster, because the intersection of two ancestor sets is again an ancestor set.~~EDIT: this is not true, the intersection of two ancestor sets may be the union of more than one ancestor set.- The current sorting algorithm (which includes the highest-feerate ancestor set among those for which the bottom transaction has a higher feerate than its ancestry) isnâ€™t exactly a composition, because the intersection of two such sets may have a bottom with low feerate.

- Merging is the composition of the union of two linearizations (with a specialized supreme subset finding algorithm).
- LIMO is a variant of composition of the input linearization plus the S_i set(s), though these sets get recomputed every iteration.