Rank-Balanced Trees

11 years 8 months ago
Rank-Balanced Trees
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.
Bernhard Haeupler, Siddhartha Sen, Robert Endre Ta
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Where WADS
Authors Bernhard Haeupler, Siddhartha Sen, Robert Endre Tarjan
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