Book ChapterDOI
Key Independent Optimality
John Iacono
- Vol. 42, Iss: 1, pp 25-31
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TLDR
It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant.Abstract:
A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, key-independent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant. Asymptotically tight upper and lower bounds are presented for key-independent optimality. Splay trees are shown to be key-independently optimal.read more
Citations
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Proceedings ArticleDOI
The geometry of binary search trees
TL;DR: It is shown that there exists an equal-cost online algorithm, transforming the conjecture of Lucas and Munro into the conjecture that the greedy algorithm is dynamically optimal, and achieving a new lower bound for searching in the BST model.
Journal ArticleDOI
Dynamic Optimality—Almost
TL;DR: This is the first major progress on Sleator and Tarjan's dynamic optimality conjecture of 1985 that O(1)-competitive binary search trees exist and presents an O(lg lg n)-competitive online binary search tree.
Posted Content
Improved Upper Bounds for Pairing Heaps
TL;DR: Pairing heaps have constant amortized time Insert and Meld as discussed by the authors, which is the same as Fibonacci heaps for all operations but decrease-key.
Journal ArticleDOI
Chain-splay trees, or, how to achieve and prove loglogN-competitiveness by splaying
TL;DR: It is proved that chain-splay is loglogN-competitive to any off-line algorithm that maintains a binary search tree with rotations, which is the nearest point to the dynamic optimality that splay trees have reached since 1983.
Book ChapterDOI
A self-adjusting data structure for multidimensional point sets
Eunhui Park,David M. Mount +1 more
TL;DR: It is shown that many of the properties enjoyed by traditional splay trees can be generalized to this multidimensional version of this self-adjusting data structure, based on a quadtree-like subdivision of space.
References
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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.
Proceedings ArticleDOI
A new representation for linear lists
TL;DR: A key idea is the construction of a number representation behaving as described above, which can be used to model the propagation of modifications in the B-tree along the finger path, with the advantage that access is cheap in the neighborhood of each finger.
Journal ArticleDOI
Design and analysis of a data structure for representing sorted lists
Mark R. Brown,Robert E. Tarjan +1 more
TL;DR: This analysis leads to a data structure for representing sorted lists when the access pattern exhibits a (perhaps time-varying) locality of reference that is substantially simpler and may be practical for lists of moderate size.
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.