red-black tree

(data structure)

Definition: A nearly-balanced tree that uses an extra bit per node to maintain balance. No leaf is more than twice as far from the root as any other.

Formal Definition: A red-black tree with n internal nodes has height at most 2log₂(n+1).

Also known as symmetric binary B-tree.

Generalization (I am a kind of ...)
B-tree.

Specialization (... is a kind of me.)
AVL tree.

Aggregate child (... is a part of or used in me.)
left rotation, right rotation.

See also height-balanced tree.

Note: The extra bit "colors" the node red or black, hence the name. These were called "symmetric binary B-trees" when first invented. The red/black naming and explanation was given by Guibas and Sedgewick.

An AVL tree is at least as balanced as a red-black tree.

Author: PEB

Implementation

analysis, explanation, examples, and code (C). Ben Pfaff's libavl (C) including pointers to other implementations. Glenn Scheper's RBSL (C) which sorts text lines using a red-black tree.

More information

explanations, examples, and links to more material.

Rudolf Bayer, Symmetric Binary B-Trees: Data Structures and Maintenance Algorithms, Acta Informatica, 1:290-306, 1972.
Leo J. Guibas and Robert Sedgewick, A Dichromatic Framework for Balanced Trees, Proceedings of the 19th Annual Symposium on Foundations of Computer Science, pages 8-21. IEEE Computer Society, 1978.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 18 August 2008.
HTML page formatted Mon Aug 25 09:01:40 2008.

Cite this as:
Paul E. Black, "red-black tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 18 August 2008. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/redblack.html