Right, the childless-descendants in an optimal chunk are always higher feerate than the chunk itself (or more generally, any “bottom” subset (a subset that includes all its descendants) must have higher feerate than the chunk itself - if not, that subset could be removed without breaking topology, and doing so would increase the feerate).
This could be the basis for another general post-processing step (e.g. try all bottom subsets of 1 or 2 transactions, and if they have lower or equal feerate than the overall chunk, split them up). Similarly for top transactions with higher or equal feerate than the overall chunk. Of course, we could also hope to build linearization algorithms that just don’t give rise to such chunkings in the first place.
FWIW, I think that relaying the set of childless-descendants for each chunk to a peer is another hypothetical way of conveying knowledge of linearizations. It could be made Erlay-compatible as it has set semantics, and with that set one can reconstruct the same linearization (and likely gives a decent result even if the clusters don’t exactly match).
Yes, absolutely. I’ve changed the text to say “could” instead of “should”. I think we’ll want to run prefix-intersection merging (or some further iteration of this idea) anytime we have distinct linearizations of the same transactions. It even works when the input linearizations don’t cover the exact same transactions but there is some overlap, though I haven’t run tests for that.