Database system concepts
An introduction to database systems: vol. 1 (5th ed.)
An introduction to database systems: vol. 1 (5th ed.)
Introduction to algorithms
Cost-optimal parallel algorithms for constructing 2-3 trees
Journal of Parallel and Distributed Computing
A unified approach to the parallel construction of search trees
Journal of Parallel and Distributed Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
A New Algorithm for the Construction of Optimal B-Trees
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
B+ retake: sustaining high volume inserts into large data pages
Proceedings of the 4th ACM international workshop on Data warehousing and OLAP
A rule based approach to network fault and security diagnosis with agent collaboration
AIS'04 Proceedings of the 13th international conference on AI, Simulation, and Planning in High Autonomy Systems
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$(a,b)$-trees are an important class of search trees. They include 2-3 trees, 2-3-4 trees, and $B$-trees as subclasses. We show that a space-minimum $(a,b)$-tree is also height-minimum and present an optimal algorithm for constructing $(a,b)$-trees that are height-minimum and space-minimum. Given $n$ keys, our algorithm constructs an $(a,b)$-tree with minimum height and fewest possible nodes. Our algorithm takes $\Theta(n)$ time if the keys in $S$ are sorted and $\Theta(n \log n )$ time if the keys are not sorted. We also discuss possible applications of our algorithm.