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Constructing Optimal Search Trees in Optimal Time
July 1999 (vol. 48 no. 7)
pp. 738-743

Abstract$(a,b)$-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.

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Index Terms:
2-3 trees, 2-3-4 trees, algorithms, $(a,b)$-trees, $B$-trees, databases, data structures, indexing, search trees, tree construction.
S.q. Zheng, M. Sun, "Constructing Optimal Search Trees in Optimal Time," IEEE Transactions on Computers, vol. 48, no. 7, pp. 738-743, July 1999, doi:10.1109/12.780881
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