Self-adjusting binary search trees
Journal of the ACM (JACM)
Sequential access in splay trees takes linear time
Combinatorica
Lower bounds for accessing binary search trees with rotations
SIAM Journal on Computing
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 Competitiveness of Linear Search
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
On the sequential access theorem and deque conjecture for splay trees
Theoretical Computer Science
O(log log n)-competitive dynamic binary search trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multi-splay trees
SIAM Journal on Computing
The geometry of binary search trees
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
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At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al. considered GREEDYFUTURE, an offline BST algorithm that greedily rearranges the search path to minimize the cost of future searches. They showed that GREEDYFUTURE is actually an online algorithm in their geometric view, and that there is a way to turn GREEDYFUTURE into an online BST algorithm with only a constant factor increase in total search cost. Demaine et al. conjectured this algorithm was dynamically optimal, but no upper bounds were given in their paper. We prove the first non-trivial upper bounds for the cost of search operations using GREEDYFUTURE including giving an access lemma similar to that found in Sleator and Tarjan's classic paper on splay trees.