Showing papers by "Rolf Fagerberg published in 1996"
TL;DR: This work analyzes B-trees with relaxed balance, and proves that each update gives rise to at most [loga(N/2)]+1 rebalancing operations, where a is the degree of the B-tree, and N is the bound on its maximal size since it was last in balance.
Abstract: B-trees with relaxed balance have been defined to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating so that extensive locking can be avoided in connection with updates. We analyze B-trees with relaxed balance, and prove that each update gives rise to at most [loga(N/2)]+1 rebalancing operations, where a is the degree of the B-tree, and N is the bound on its maximal size since it was last in balance. Assuming that the size of nodes is at least twice the degree, we prove that rebalancing can be performed in amortized constant time. So, in the long run, rebalancing is constant time on average, even if any particular update could give rise to a logarithmic number of rebalancing operations. We also prove that the amount of rebalancing done at any particular level decreases exponentially going from the leaves towards the root. This is important since the higher up in the tree a lock due to a rebalancing operation occurs, the larger a subtree which cannot be accessed by other processes for the duration of that lock. All of these results are in fact obtained for the more general (a, b)-trees, so we have results for both of the common B-tree versions as well as 2-3 trees and 2-3-4 trees.
24 citations
TL;DR: A generalization of binomial queues is presented, the definition of which involves a freely chosen sequence of integers greater than one that leads to different worst case bounds for the priority queue operations, allowing the user to adapt the data structure to the needs of a specific application.
8 citations
03 Jul 1996
TL;DR: It is proved that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n) can guarantee a height smaller than [log(n + 1) + 1/ f(n)] for all n, and the existing upper bound for worst case algorithms is improved.
Abstract: We prove that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n)) can guarantee a height smaller than [log(n + 1) + 1/f(n)] for all n. We improve the existing upper bound to [log(n + 1) + log2 (f(n))/f(n)], thus almost matching our lower bound. We also improve the existing upper bound for worst case algorithms, and give a lower bound for the semi-dynamic case.
6 citations
01 Jun 1996
TL;DR: A simple implementation of meldable priority queues, achieving Insert, FindMin, and Meld in O(1) worst case time, and DeleteMin and Delete in O (log n) best case time is given.
Abstract: We give a simple implementation of meldable priority queues, achieving Insert, FindMin, and Meld in O(1) worst case time, and DeleteMin and Delete in O(log n) worst case time.
3 citations