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Issue No. 07 - July (1999 vol. 48)
ISSN: 0018-9340
pp: 738-743
<p><b>Abstract</b>—<tmath>$(a,b)$</tmath>-trees are an important class of search trees. They include 2-3 trees, 2-3-4 trees, and <tmath>$B$</tmath>-trees as subclasses. We show that a space-minimum <tmath>$(a,b)$</tmath>-tree is also height-minimum and present an optimal algorithm for constructing <tmath>$(a,b)$</tmath>-trees that are height-minimum and space-minimum. Given <tmath>$n$</tmath> keys, our algorithm constructs an <tmath>$(a,b)$</tmath>-tree with minimum height and fewest possible nodes. Our algorithm takes <tmath>$\Theta(n)$</tmath> time if the keys in <tmath>$S$</tmath> are sorted and <tmath>$\Theta(n \log n )$</tmath> time if the keys are not sorted. We also discuss possible applications of our algorithm.</p>
2-3 trees, 2-3-4 trees, algorithms, $(a, b)$-trees, $B$-trees, databases, data structures, indexing, search trees, tree construction.

S. Zheng and M. Sun, "Constructing Optimal Search Trees in Optimal Time," in IEEE Transactions on Computers, vol. 48, no. , pp. 738-743, 1999.
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