AVL trees, red-black trees, and others. Weak AVL (wavl) trees are a
recently discovered member of that class. This change replaces
red-black rebalancing with weak AVL rebalancing in the RB tree macros.
Wavl trees sit between AVL and red-black trees in terms of how
strictly balance is enforced. They have the stricter balance of AVL
trees as the tree is built - a wavl tree is an AVL tree until the
first deletion. Once removals start, wavl trees are lazier about
rebalancing than AVL trees, so that removals can be fast, but the
balance of the tree can decay to that of a red-black tree. Subsequent
insertions can push balance back toward the stricter AVL conditions.
Removing a node from a wavl tree never requires more than two
rotations, which is better than either red-black or AVL
trees. Inserting a node into a wavl tree never requires more than two
rotations, which matches red-black and AVL trees. The only
disadvantage of wavl trees to red-black trees is that more insertions
are likely to adjust the tree a bit. That's the cost of keeping the
tree more balanced.
Testing has shown that for the cases where red-black trees do worst,
wavl trees better balance leads to faster lookups, so that if lookups
outnumber insertions by a nontrivial amount, lookup time saved exceeds
the extra cost of balancing.
Reviewed by: alc, gbe, markj
Tested by: pho
Discussed with: emaste
Differential Revision: https://reviews.freebsd.org/D25480
504ba65c8c