Amortized analyses of self-organizing sequential search heuristics
Communications of the ACM - Lecture notes in computer science Vol. 174
Data structures and network algorithms
Data structures and network algorithms
Self-adjusting binary search trees
Journal of the ACM (JACM)
Journal of Algorithms
Self-Organizing Binary Search Trees
Journal of the ACM (JACM)
Design of Dynamic Data Structures
Design of Dynamic Data Structures
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
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
Splay trees, Davenport-Schinzel sequences, and the deque conjecture
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On embedding subclasses of height-balanced trees in hypercubes
Information Sciences: an International Journal
How to splay for loglogn-competitiveness
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
De-amortizing binary search trees
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We give a new lemma (dynamic reweighing) about splay trees and we define a class of dynamically self-adjusted trees (parametrically balanced) wide enough to include BB(α), AVL, rank-balanced and B-trees. Using our lemma we prove that splay trees are competitive to any such class of dynamic trees-noticing that so far splay trees had been proven competitive only w.r.t, static structures like trees and sorted tables with a finger, or exponentially faster than dynamic linear structures like a 'move-to-front' self-adjusting list. (Note: A class of dynamic trees achieving the dynamic finger property can be designed, and splay trees have been shown to have this property also.) Finally, we extend these results to generalized splay trees.