Self-adjusting binary search trees
Journal of the ACM (JACM)
Sequential access in splay trees takes linear time
Combinatorica
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Approximate closest-point queries in high dimensions
Information Processing Letters
Journal of Algorithms
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
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
Computational Geometry: Theory and Applications
Closest-point problems simplified on the RAM
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
Distribution-sensitive data structures
Distribution-sensitive data structures
On the sequential access theorem and deque conjecture for splay trees
Theoretical Computer Science
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
O(log log n)-competitive dynamic binary search trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A simple entropy-based algorithm for planar point location
ACM Transactions on Algorithms (TALG)
A unified access bound on comparison-based dynamic dictionaries
Theoretical Computer Science
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
Chain-splay trees, or, how to achieve and prove loglogN-competitiveness by splaying
Information Processing Letters
Splay trees, Davenport-Schinzel sequences, and the deque conjecture
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th 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
A dynamic data structure for approximate range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
Geometric Approximation Algorithms
Geometric Approximation Algorithms
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A data structure is said to be self-adjusting if it dynamically reorganizes itself to adapt to the pattern of accesses. Efficiency is typically measured in terms of amortized complexity, that is, the average running time of an access over an arbitrary sequence of accesses. The best known example of such a data structure is Sleator and Tarjan's splay tree. In this paper, we introduce a self-adjusting data structure for storing multidimensional point data. The data structure is based on a quadtree-like subdivision of space. Like a quadtree, the data structure implicitly encodes a subdivision of space into cells of constant combinatorial complexity. Each cell is either a quadtree box or the set-theoretic difference of two such boxes. Similar to the traditional splay tree, accesses are based on an splaying operation that restructures the tree in order to bring an arbitrary internal node to the root of the tree. We show that many of the properties enjoyed by traditional splay trees can be generalized to this multidimensional version.