It's pretty trivial to have the client hit the root on startup, and then cache that and never make another call. API roots don't change very much.
> First, are there then multiple roots?
Nope. Here's an example of what I call the 'hypermedia proxy pattern' in Sinatra: https://gist.github.com/3172911
I based this off of this talk by Jon Moore: https://vimeo.com/20781278 and demo'd it at the end of this presentation: http://oredev.org/2012/sessions/designing-hypermedia-apis
Basically, you can fold elements of the collection up into the parent, and the client will automatically make less requests. Jon's presentation goes from 14 requests for the first iteration to 2 on the first hit, 1 every hit thereafter, with no changes to the client.
> when your data is hierarchical, it's nice for other reasons to reflect this in your URI structure.
Sure! So provide both: one 'deep link' or full collection in the root (or wherever) response, but also serve the data as a separate resource that's hierarchical. Best of both worlds.