Topic
Binary search tree
About: Binary search tree is a research topic. Over the lifetime, 1640 publications have been published within this topic receiving 34824 citations. The topic is also known as: BST & ordered binary tree.
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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.
Abstract: The splay tree, a self-adjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an n-node splay tree, all the standard search tree operations have an amortized time bound of O(log n) per operation, where by “amortized time” is meant the time per operation averaged over a worst-case sequence of operations. Thus splay trees are as efficient as balanced trees when total running time is the measure of interest. In addition, for sufficiently long access sequences, splay trees are as efficient, to within a constant factor, as static optimum search trees. The efficiency of splay trees comes not from an explicit structural constraint, as with balanced trees, but from applying a simple restructuring heuristic, called splaying, whenever the tree is accessed. Extensions of splaying give simplified forms of two other data structures: lexicographic or multidimensional search trees and link/cut trees.
1,321 citations
TL;DR: The proof to be given is relatively simple and the importance of this result can be measured in terms of the Jarge amount of effort that has been put into fmding efftient aJgorJthms for constructing optimal binary decision trees.
1,014 citations
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TL;DR: In this paper, a simple dictionary with worst case constant lookup time was presented, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al.
Abstract: We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. [SIAM J. Comput. 23 (4) (1994) 738-761]. The space usage is similar to that of binary search trees. Besides being conceptually much simpler than previous dynamic dictionaries with worst case constant lookup time, our data structure is interesting in that it does not use perfect hashing, but rather a variant of open addressing where keys can be moved back in their probe sequences. An implementation inspired by our algorithm, but using weaker hash functions, is found to be quite practical. It is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee on lookup time.
963 citations
01 Nov 1986
TL;DR: This paper develops simple, systematic, and efficient techniques for making linked data structures persistent, and uses them to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O (1) space bounds for insertion and deletion.
Abstract: This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any time. We develop simple, systematic, and efficient techniques for making linked data structures persistent. We use our techniques to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O (1) space bounds for insertion and deletion.
866 citations
17 Aug 1989
TL;DR: This paper describes and analyzes skip lists and presents new techniques for analyzing probabilistic algorithms.
Abstract: Skip lists are a practical, probabilistic data structure that can be used in place of balanced trees. Algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees. This paper describes and analyzes skip lists and presents new techniques for analyzing probabilistic algorithms.
843 citations