De-amortizing binary search trees

Authors:
Prosenjit Bose;Sébastien Collette;Rolf Fagerberg;Stefan Langerman
Affiliations:
School of Computer Science, Carleton University, Canada;Département d'Informatique, Université Libre de Bruxelles, Belgium;Department of Mathematics and Computer Science, University of Southern Denmark, Denmark;Département d'Informatique, Université Libre de Bruxelles, Belgium
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Year:
2012

Citing 17
Cited 1

Self-adjusting binary search trees

Journal of the ACM (JACM)
Lower bounds for accessing binary search trees with rotations

SIAM Journal on Computing
Self-Organizing Binary Search Trees

Journal of the ACM (JACM)
Alternatives to splay trees with O(log n) worst-case access times

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences

SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof

SIAM Journal on Computing
Splay trees: a reweighing lemma and a proof of competitiveness vs. dynamic balanced trees

Journal of Algorithms
O(log log n)-competitive dynamic binary search trees

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A unified access bound on comparison-based dynamic dictionaries

Theoretical Computer Science
Dynamic Optimality—Almost

SIAM Journal on Computing
Chain-splay trees, or, how to achieve and prove loglogN-competitiveness by splaying

Information Processing Letters
Dynamic optimality for skip lists and B-trees

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A dichromatic framework for balanced trees

SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
The geometry of binary search trees

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Skip-Splay: Toward Achieving the Unified Bound in the BST Model

WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Layered working-set trees

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
An O(log log n)-competitive binary search tree with optimal worst-case access times

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory

Combining binary search trees

ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a general method for de-amortizing essentially any Binary Search Tree (BST) algorithm. In particular, by transforming Splay Trees, our method produces a BST that has the same asymptotic cost as Splay Trees on any access sequence while performing each search in O(logn) worst case time. By transforming Multi-Splay Trees, we obtain a BST that is O(loglogn) competitive, satisfies the scanning theorem, the static optimality theorem, the static finger theorem, the working set theorem, and performs each search in O(logn) worst case time. Transforming OPT proves the existence of an O(1)-competitive offline BST algorithm which performs at most O(log n) BST operations between each access to the keys in the input sequence. Finally, we obtain that if there is an O(1)-competitive online BST algorithm, then there is also one that performs every search in O(logn) operations worst case.