AVL-trees for localized search
Information and Control
A balanced search tree with O(1) worst case update time
Acta Informatica
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Eliminating amortization: on data structures with guaranteed response time
Eliminating amortization: on data structures with guaranteed response time
A constant update time finger search tree
Information Processing Letters
Finger search trees with constant insertion time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Tight(er) worst-case bounds on dynamic searching and priority queues
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Optimal finger search trees in the pointer machine
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Localized search in sorted lists
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
A new representation for linear lists
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
A programming and problem-solving seminar
A programming and problem-solving seminar
Amortized rigidness in dynamic cartesian trees
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Partially persistent B-trees with constant worst-case update time
Computers and Electrical Engineering
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We present new search trees with worst-case O(1) update time and O(log n) search time, storing n elements in linear space, in the Pointer Machine (PM) model of computation. In addition, these trees can easily support finger searches in time O(log d) and update operations in worst-case O(log* n) time. The parameter d represents the number of elements (distance) between the search element and an element pointed to by a pointer termed finger. Our data structure is based on a previous result by Fleischer that exhibits the same asymptotic time and space complexities for simple search trees. We improve on this result by handling deletions in an explicit way without using the standard trick of global rebuilding. This is the first search tree that combines worst-case update times with a local rebalancing scheme without using global rebuilding to tackle deletions. In addition, insight is acquired from the construction of these trees as to why deletions are considered more difficult than insertions in the (a,b)-trees setting. Finally, we hope that these techniques may lead to a simpler version of the constant update finger search tree presented recently by Brodal et al. [5].