Abstract
An algorithm is presented which constructs an optimal binary search tree for an ordered list of n items, and which requires subquadratic time if there is no long sublist of very low frequency items. For example, time = O( n 1.6) if the frequency of each item is at least ε n for some constant ε > 0. A second algorithm is presented which constructs an approximately optimal binary search tree. This algorithm has one parameter, and exhibits a trade-off between speed and accuracy. It is possible to choose the parameter such that time = O( n 1.6) and error = o(1).
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