Optimal integer alphabetic trees in linear time

Authors:
T. C. Hu;Lawrence L. Larmore;J. David Morgenthaler
Affiliations:
Department of Computer Science and Engineering, University of California, San Diego, CA;Department of Computer Science, University of Nevada, Las Vegas, NV;Applied Biosystems, Foster City, CA
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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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 [6] 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.