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All of the red-black tree algorithms that have been proposed are characterized by a worst-case search time bounded by a small constant multiple of log N in a tree of N keys, and the behavior observed in practice is typically that same multiple faster than the worst-case bound, close to the optimal log N nodes examined that would be observed in a perfectly balanced tree.
Parallel algorithms for constructing red–black trees from sorted lists of items can run in constant time or ( ) time, depending on the computer model, if the number of processors available is asymptotically proportional to the number of items where . Fast search, insertion, and deletion parallel algorithms are also known.
AA trees are named after their originator, Swedish computer scientist Arne Andersson. [1] AA trees are a variation of the red–black tree, a form of binary search tree which supports efficient addition and deletion of entries. Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild.
A schematic picture of the skip list data structure. Each box with an arrow represents a pointer and a row is a linked list giving a sparse subsequence; the numbered boxes (in yellow) at the bottom represent the ordered data sequence.
2–3–4 trees are B-trees of order 4; [1] like B-trees in general, they can search, insert and delete in O(log n) time.One property of a 2–3–4 tree is that all external nodes are at the same depth.
In AVL trees, each deletion may require a logarithmic number of tree rotation operations, while red–black trees have simpler deletion operations that use only a constant number of tree rotations. WAVL trees, like red–black trees, use only a constant number of tree rotations, and the constant is even better than for red–black trees. [1] [2]
To turn a regular search tree into an order statistic tree, the nodes of the tree need to store one additional value, which is the size of the subtree rooted at that node (i.e., the number of nodes below it). All operations that modify the tree must adjust this information to preserve the invariant that size[x] = size[left[x]] + size[right[x]] + 1
I am tempted to remove some of the "See also" links. AA trees are a variation of the red-black tree, AVL and B-trees are discussed in the article, but scapegoat trees, splay trees, and T-trees are not. The article about scapegoat trees mentions red-black trees, but the connection is weak. The other two don't refer to red-black trees at all.