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
On-the-fly optimization of data structures
Communications of the ACM
AVL trees with relaxed balance
Journal of Computer and System Sciences
Advances in Algorithms, Languages, and Complexity
Advances in Algorithms, Languages, and Complexity
Data Structures and Algorithms
Data Structures and Algorithms
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
Exponentially Decreasing Number of Operations in Balanced Trees
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
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
Concurrent rebalancing on HyperRed-Black trees
SCCC '97 Proceedings of the 17th International Conference of the Chilean Computer Science Society
Relaxed Balancing Made Simple
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Exponentially Decreasing Number of Operations in Balanced Trees
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
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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.