Complexity of Layered Binary Search Trees with Relaxed Balance
نویسندگان
چکیده
When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speed-up in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed structures. In our opinion, one of the simplest and most intuitive presentations of balanced search trees has been given via layered trees. We show that relaxed layered trees are among the best of the relaxed structures. More precisely, rebalancing is worst-case logarithmic and amortized constant per update, and restructuring is worst-case constant per update.
منابع مشابه
Variants of ( a ; b ) - Trees with Relaxed
New variants of (a; b)-trees with relaxed balance are proposed. These variants have better space utilization than the earlier proposals, while the asymptotic complexity of rebalancing is unchanged. The proof of complexity , which is derived, is much simpler than the ones previously published. Through experiments, some of the most interesting applications of this data structure are modeled, and ...
متن کاملAVL Trees with Relaxed Balance
The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in main-memory databases. In this paper, we describe a relaxed version of AVL trees. We prove that each update gives rise to at most a logarithmic number of rebalancing operations and that the number of rebalancing operations in the semidynamic case is amortized c...
متن کاملB-slack trees: Highly Space Efficient B-trees
B-slack trees, a subclass of B-trees that have substantially better worst-case space complexity, are introduced. They store n keys in height O(logb n), where b is the maximum node degree. Updates can be performed in O(log b 2 n) amortized time. A relaxed balance version, which is well suited for concurrent implementation, is also presented.
متن کاملB-slack Trees: Space Efficient B-Trees
B-slack trees, a subclass of B-trees that have substantially better worst-case space complexity, are introduced. They store n keys in height O(logb n), where b is the maximum node degree. Updates can be performed in O(log b 2 n) amortized time. A relaxed balance version, which is well suited for concurrent implementation, is also presented.
متن کاملB-trees with relaxed balance
B-trees with relaxed balance have been deened to facilitate fast updating in a concurrent database environment. In that structure, updating and rebalancing are uncoupled such that extensive locking can be avoided in connection with updates. Constraints, weaker than the usual ones, are maintained such that the tree can still be balanced independent of the updating processes. We nd the idea of re...
متن کامل