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
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Persistence, amortization and randomization
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Amortization results for chromatic search trees, with an application to priority queues
Journal of Computer and System Sciences
Complexity of Layered Binary Search Trees with Relaxed Balance
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
On the Existence and Construction of Non-Extreme (a,b)-Trees
On the Existence and Construction of Non-Extreme (a,b)-Trees
Complexity of Layered Binary Search Trees with Relaxed Balance
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
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While many tree-like structures have been proven to support amortized constant number of operations after updates, considerably fewer structures have been proven to support the more general exponentially decreasing number of operations with respect to distance from the update. In addition, all existing proofs of exponentially decreasing operations are tailor-made for specific structures. We provide the first formalization of conditions under which amortized constant number of operations imply exponentially decreasing number of operations. Since our proof is constructive, we obtain the constants involved immediately. Moreover, we develop a number of techniques to improve these constants.