De-amortizing binary search trees
Prosenjit Bose,Sébastien Collette,Rolf Fagerberg,Stefan Langerman +3 more
- pp 121-132
Reads0
Chats0
TLDR
In this article, a general method for de-amortizing essentially any Binary Search Tree (BST) algorithm is presented, which has the same asymptotic cost as Splay Trees on any access sequence while performing each search in O(logn) worst case time.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.read more
Citations
More filters
Book ChapterDOI
In Pursuit of the Dynamic Optimality Conjecture
TL;DR: In this article, the authors survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal.
Proceedings ArticleDOI
Weighted dynamic finger in binary search trees
John Iacono,Stefan Langerman +1 more
TL;DR: This result is the strongest finger-type bound to be proven for binary search trees, and compared to the previous proof of the dynamic finger bound for Splay trees, it is significantly shorter, stronger, simpler, and has reasonable constants.
Book ChapterDOI
Combining binary search trees
TL;DR: In this paper, the authors presented a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time of the given BSTs, for any online access sequence.
Posted Content
New Paths from Splay to Dynamic Optimality
Caleb Levy,Robert E. Tarjan +1 more
TL;DR: This work attempts to lay the foundations for a proof of the dynamic optimality conjecture, which is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches.
References
More filters
Journal ArticleDOI
Self-adjusting binary search trees
TL;DR: The splay tree, a self-adjusting form of binary search tree, is developed and analyzed and is found to be as efficient as balanced trees when total running time is the measure of interest.
An algorithm for the organization of information
TL;DR: The organization of information placed in the points of an automatic computer is discussed and the role of memory, storage and retrieval in this regard is discussed.
Proceedings ArticleDOI
A dichromatic framework for balanced trees
TL;DR: This paper shows how to imbed in this framework the best known balanced tree techniques and then use the framework to develop new algorithms which perform the update and rebalancing in one pass, on the way down towards a leaf.
Journal ArticleDOI
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
TL;DR: On an n-node splay tree, the amortized cost of an access at distance d from the preceding access is O(log (d+1)) and there is an O(n) initialization cost.