Planar point location using persistent search trees
Communications of the ACM
An amortized analysis of insertions into AVL trees
SIAM Journal on Computing
Concurrency control in database structures with relaxed balance
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Uncoupling updating and rebalancing in chromatic binary search trees
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Regular Article: Efficient rebalancing of chromatic search trees
Proceedings of the 30th IEEE symposium on Foundations of computer science
Amortization results for chromatic search trees, with an application to priority queues
Journal of Computer and System Sciences
Group updates for relaxed height-balanced trees
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Analysis and performance of inverted data base structures
Communications of the ACM
AVL trees with relaxed balance
Journal of Computer and System Sciences
Concurrency Control in B-Trees with Batch Updates
IEEE Transactions on Knowledge and Data Engineering
Hybrid Index Organizations for Text Databases
EDBT '92 Proceedings of the 3rd International Conference on Extending Database Technology: Advances in Database Technology
AVL Trees with Relaxed Balance
Proceedings of the 8th International Symposium on Parallel Processing
Efficient Rebalancing of Chromatic Search Trees
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Amortization Results for Chromatic Search Trees, with an Application to Priority Queues
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Relaxed Balance through Standard Rotations
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Concurrent Rebalancing of ACL Trees: A Fine-Grained Approach (Extended Abstract)
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
Relaxed Balance for Search Trees with Local Rebalancing
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Relaxed Balanced Red-Black Trees
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
IPPS '95 Proceedings of the 9th International Symposium on Parallel Processing
On the existence and construction of non-extreme (a, b)-trees
Information Processing Letters
Amortized Complexity of Bulk Updates in AVL-Trees
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Single and bulk updates in stratified trees: an amortized and worst-case analysis
Computer Science in Perspective
Handling frequent updates of moving objects
Proceedings of the 14th ACM international conference on Information and knowledge management
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Data structures with relaxed balance differ from standard structures in that rebalancing can be delayed and interspersed with updates. This gives extra flexibility in both sequential and parallel applications.We study the version of multi-way trees called (a,b)-trees (which includes B-trees) with the operations insertion, deletion, and group insertion. The latter has applications in for instance document databases and WWW search engines. We prove that we obtain the optimal asymptotic rebalancing complexities of amortized constant time for insertion and deletion and amortized logarithmic time in the size of the group for group insertion. These results hold even for the relaxed version.Our results also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results in the most interesting cases.