Date: 29 May 2005

The Optimal Alphabetic Tree problem revisited

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The Optimal Alphabetic Binary Tree (OABT) problem is equivalent to the Optimal Binary Search Tree problem with the restriction that all data are in the leaves. The problem can be solved in O(n log n) time, while the best known lower bound is Ω(n).

The main result of this paper is an O(n√log n)-time algorithm for the integer OABT problem. As a side effect we obtain an O(n log k)-time algorithm for the general OABT problem, where k is a number at most as large as the number of local minima. This algorithm gives rise to linear time algorithms for some special cases. As a corollary, we obtain an O(nL)-time algorithm for the integer case of the optimal height-limited alphabetic tree problem, where L is the height limitation.