Optimal bounds on the dictionary problem
Proceedings of the international symposium on Optimal algorithms
Binary search trees of almost optimal height
Acta Informatica
Efficient maintenance of binary search trees
Efficient maintenance of binary search trees
Fast Updating of Well-Balanced Trees
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
Binary Search Trees: How Low Can You Go?
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Updating Almost Complete Trees or One Level Makes All the Difference
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Comparison-Efficient And Write-Optimal Searching and Sorting
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
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For any function f, we give a rebalancing scheme for binary search trees which uses amortized O(f(n)) work per update while maintaining a height bounded by ⌊log(n + 1) + 1/f(n)⌋. This improves on previous algorithms for maintaining binary search trees of very small height, and matches an existing lower bound. The main implication is the exact characterization of the amortized cost of rebalancing binary search trees, seen as a function of the height bound maintained. We also show that in the semi-dynamic case, a height of ⌊log(n+1)⌋ can be maintained with amortized O(log n) work per insertion. This implies new results for TreeSort, and proves that it is optimal among all comparison based sorting algorithms for online sorting.