A note on the height of binary search trees
Journal of the ACM (JACM)
On the average internal path length of many search trees
Acta Informatica
Branching processes in the analysis of the heights of trees
Acta Informatica
On the Variance of the Height of Random Binary Search Trees
SIAM Journal on Computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Variance of the height of binary search trees
Theoretical Computer Science
Constant bounds on the moments of the height of binary search trees
Theoretical Computer Science
On the Concentration of the Height of Binary Search Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
The height of a random binary search tree
Journal of the ACM (JACM)
The Variance of the height of binary search trees
Theoretical Computer Science
The height of a binary search tree: the limiting distribution perspective
Theoretical Computer Science
The height of a random binary search tree
Journal of the ACM (JACM)
On Robson's convergence and boundedness conjectures concerning the height of binary search trees
Theoretical Computer Science
Extremal Weighted Path Lengths In Random Binary Search Trees
Probability in the Engineering and Informational Sciences
Smoothed analysis of binary search trees
Theoretical Computer Science
Smoothed Analysis of Binary Search Trees and Quicksort under Additive Noise
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Smoothed analysis of binary search trees
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Smoothed analysis of left-to-right maxima with applications
ACM Transactions on Algorithms (TALG)
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It is shown that all centralized absolute moments E|Hn − EHn|α (α ≥ 0) of the height Hn of binary search trees of size n and of the saturation level Hn′ are bounded. The methods used rely on the analysis of a retarded differential equation of the form Φ′(u) = −α−2Φ(u/α)2 with α 1. The method can also be extended to prove the same result for the height of m-ary search trees. Finally the limiting behaviour of the distribution of the height of binary search trees is precisely determined.