The algorithm design manual
Balanced Search Trees Made Simple
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Binary B-trees for virtual memory
SIGFIDET '71 Proceedings of the 1971 ACM SIGFIDET (now SIGMOD) Workshop on Data Description, Access and Control
Deletion without Rebalancing in Multiway Search Trees
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Deletion without rebalancing in balanced binary trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Skip lift: a probabilistic alternative to red-black trees
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Skip lift: A probabilistic alternative to red-black trees
Journal of Discrete Algorithms
Deletion without rebalancing in multiway search trees
ACM Transactions on Database Systems (TODS)
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Since the invention of AVL trees in 1962, a wide variety of ways to balance binary search trees have been proposed. Notable are red-black trees, in which bottom-up rebalancing after an insertion or deletion takes O(1) amortized time and O(1) rotations worst-case. But the design space of balanced trees has not been fully explored. We introduce the rank-balanced tree , a relaxation of AVL trees. Rank-balanced trees can be rebalanced bottom-up after an insertion or deletion in O(1) amortized time and at most two rotations worst-case, in contrast to red-black trees, which need up to three rotations per deletion. Rebalancing can also be done top-down with fixed lookahead in O(1) amortized time. Using a novel analysis that relies on an exponential potential function, we show that both bottom-up and top-down rebalancing modify nodes exponentially infrequently in their heights.