Optimal binary search trees
Włodzimierz Dobosiewicz
Abstract
Włodzimierz Dobosiewicz
Abstract
Optimal binary search trees are described in practically every textbook on data structures. It is commonly accepted that since the publication of the paper by Knuth everything about them is known and understood. This paper shows that it is not necessarily so, and that, in particular, “optimal binary search trees” as normally defined are not optimal at all. Various types of optimal split trees are more efficient than optimal search trees as defined by Knuth.
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Optimal binary search trees are described in practically every textbook on data structures. It is commonly accepted that since the publication of the paper by Knuth everything about them is known and understood. This paper shows that it is not necessarily so, and that, in particular, “optimal binary search trees” as normally defined are not optimal at all. Various types of optimal split trees are more efficient than optimal search trees as defined by Knuth.
Key concepts: Binary search tree, Optimal binary search tree, Mathematics, Ternary search tree, Random binary tree, Weight-balanced tree, Binary number, Binary search algorithm