A note on the height of binary search trees
Journal of the ACM (JACM)
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Journal of Computer and System Sciences
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On the Variance of the Height of Random Binary Search Trees
SIAM Journal on Computing
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SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Constant bounds on the moments of the height of binary search trees
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Heuristics for semirandom graph problems
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Data Structures and Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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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)
An analytic approach to the height of binary search trees II
Journal of the ACM (JACM)
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
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ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
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ACM Transactions on Algorithms (TALG)
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Binary search trees are one of the most fundamental data structures. While the height of such a tree may be linear in the worst case, the average height with respect to the uniform distribution is only logarithmic. The exact value is one of the best studied problems in average-case complexity. We investigate what happens in between by analysing the smoothed height of binary search trees: Randomly perturb a given (adversarial) sequence and then take the expected height of the binary search tree generated by the resulting sequence. As perturbation models, we consider partial permutations, partial alterations, and partial deletions. On the one hand, we prove tight lower and upper bounds of roughly @Q((1-p)@?n/p) for the expected height of binary search trees under partial permutations and partial alterations, where n is the number of elements and p is the smoothing parameter. This means that worst-case instances are rare and disappear under slight perturbations. On the other hand, we examine how much a perturbation can increase the height of a binary search tree, i.e. how much worse well balanced instances can become.