Chapter

Algorithms – ESA 2005

Volume 3669 of the series Lecture Notes in Computer Science pp 226-237

Optimal Integer Alphabetic Trees in Linear Time

  • T. C. HuAffiliated withDepartment of Computer Science and Engineering, University of California
  • , Lawrence L. LarmoreAffiliated withDepartment of Computer Science, University of Nevada
  • , J. David MorgenthalerAffiliated withApplied Biosystems

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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.