Note that because we amortize the traversal cost over the number of
entries, mtree traversal may have some strange looking results when
compared to mtree lookup.
Though it's interesting to note this is a valid result. In mtree lookups
we need to fetch the mdir for each entry, which is expensive. However
mtree traversal can strictly avoid fetching each mdir more than once.
This does make mdir traversal faster when iterating over all mdirs in
order.
This can be represented in big O notation if we treat the number of
entries (n) and block size (b) as variables:
- mtree traversal via lookup = O(nb+nlog(b)logb(n))
- mtree traversal via traversal = O(nlog(b)logb(n))
It's interesting to note the different performance characteristics of
purely CoW btrees vs our mutable mtree.
The main downside of our mtree is the need to fetch leaf mdirs. This
fetch is expensive, and can be avoided in CoW btrees by storing the
trunk in each branch's parent.
On the other hand, btrees need to propagate all changes upwards to the
root.
An interesting takeaway is that a sort of mdir-trunk cache may be a very
interesting optimization for relatively little RAM cost. This may be
something to explore in the future.
Christopher Haster