Data structures and network algorithms
Data structures and network algorithms
Self-adjusting binary search trees
Journal of the ACM (JACM)
Rotation distance, triangulations, and hyperbolic geometry
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Sequential access in splay trees takes linear time
Combinatorica
Lower bounds for accessing binary search trees with rotations
SIAM Journal on Computing
Static optimality and dynamic search-optimality in lists and trees
SODA '02 Proceedings of the thirteenth 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
On the sequential access theorem and deque conjecture for splay trees
Theoretical Computer Science
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
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
Upper bounds for maximally greedy binary search trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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
Poketree: a dynamically competitive data structure with good worst-case performance
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
De-amortizing binary search trees
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A self-adjusting data structure for multidimensional point sets
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The Dynamic Optimality Conjecture [ST85] states that splay trees are competitive (within a constant competitive factor) among the class of all binary search tree (BST) algorithms. Despite 20 years of research this conjecture is still unresolved. Recently, Demaine et al. [DHIP04] suggested searching for alternative algorithms which have small but non-constant competitive factors. They proposed Tango, a BST algorithm which is nearly dynamically optimal - its competitive ratio is O(log log n) instead of a constant. Unfortunately, for many access patterns, such as random and sequential, Tango is worse than other BST algorithms by a factor of log log n.In this paper, we introduce the multi-splay tree (MST) data structure, which is the first O(log log n)-competitive BST to simultaneously achieve O(log n) amortized cost and O(log2 n) worst-case cost per query. We also prove the sequential access lemma for MSTs, which states that sequentially accessing all keys takes linear time. Thus, MSTs are O(log log n)-competitive like Tango but, unlike Tango, require only O(log n) amortized time per access in an arbitrary sequence and only O(1) amortized time per access during a sequential access sequence.Furthermore, we generalize the standard framework for competitive analysis of BST algorithms to include updates (insertions and deletions) in addition to queries. In doing so, we extend the lower bound of Wilber [Wil89] and Demaine et al. [DHIP04] to handle these update operations. We show how MSTs can be modified to support these update operations and be O(log log n)-competitive in the new framework while maintaining the rest of the properties above.