Planar point location using persistent search trees
Communications of the ACM
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
AVL trees with relaxed balance
Journal of Computer and System Sciences
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
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We introduce the relaxed k-tree, a search tree with relaxed balance and a height bound, when in balance, of (1 + Ɛ) log2 n + 1, for any Ɛ 0. The rebalancing work is amortized O(1/Ɛ) per update. This is the first binary search tree with relaxed balance having a height bound better than c ċ log2 n for a fixed constant c. In all previous proposals, the constant is at least 1/ log2 Φ 1.44, where Φ is the golden ratio. As a consequence, we can also define a standard (non-relaxed) k-tree with amortized constant rebalancing per update, which is an improvement over the original definition. Search engines based on main-memory databases with strongly fluctuating workloads are possible applications for this line of work.