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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Haeupler, B., Sen, S., & Tarjan, R. E. (2009). Rank-balanced trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5664 LNCS, pp. 351–362). https://doi.org/10.1007/978-3-642-03367-4_31
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