idea.txt

Load balancer returns mapping of hub ids to processor ranks. This mapping is
global and stored on all processors. The idea then is that when we do radii
queries, the descent down the replicated portion of the tree should eventually
reach vertices that are not stored in the replicated tree but only on particular
processors. Recall that hub ids correspond one-to-one to the vertices whose
associated point is the hub representative and whose descendants are all in the hub.
Therefore, we can use the load balancer mapping (hub ids to processor ranks) to determine
which processor stores the hub descendants.

A nice way of doing this in parallel is to handle batches of query points. Then all processors
can work in parallel to handle a partition of the batch and each partition will then determine
which of the local subtrees to send batches of its query points.

There is then an all-to-all collective that sends all points to their local subtree owning
processors. Once each local processor has received its local batched queries, we lookup
which local cover tree corresponds to the hub that the vertex should be coming from, and
query against that cover tree. To get the correct results, we must store a mapping of
of the local tree point indices to the global tree indices. This can be accomplished by
storing a vector for each local cover tree that maps the local indices to the original
global indices.