RB tree VS AVL tree

AVL trees are actually easier to implement than RB trees because there are fewer cases. And AVL trees require O(1) rotations on an insertion, whereas red-black trees require O(lgn).
In practice, the speed of AVL trees versus red-black trees will depend on the data that you're inserting. If your data is well distributed, so that an unbalanced binary tree would generally be acceptable (i.e. roughly in random order), but you want to handle bad cases anyway, then red-black trees will be faster because they do less unnecessary rebalancing of already acceptable data.On the other hand, if a pathological insertion order (e.g. increasing order of key) is common, then AVL trees will be faster, because the stricter balancing rule will reduce the tree's height.
Splay trees might be even faster than either RB or AVL trees,depending on your data access distribution. And if you can use a hash instead of a tree, then that'll be fastest of all.

 

 

B-tree when you're managing more than thousands of items and you're paging them from a disk or some slow storage medium.

RB tree when you're doing fairly frequent inserts, deletes and retrievals on the tree.

AVL tree when your inserts and deletes are infrequent relative to your retrievals.