Optimal integer alphabetic trees in linear time

Abstract

We show that optimal alphabetic binary trees can be constructed in O(n) time if the elements of the initial sequence are drawn from a domain that can be sorted in linear time. We describe a hybrid algorithm that combines the bottom-up approach of the original Hu-Tucker algorithm with the top-down approach of Larmore and Przytycka's Cartesian tree algorithms. The hybrid algorithm demonstrates the computational equivalence of sorting and level tree construction. © Springer-Verlag Berlin Heidelberg 2005.