Rochester Institute of Technology
Computer Science Department



HU-TUCKER ALGORITHM FOR BUILDING OPTIMAL ALPHABETIC BINARY SEARCH TREES


by
Sashka T. Davis



A thesis, submitted to
The Faculty of the Department of Computer Science,
in partial fulfillment of the requirements for the degree of
Master of Science in Computer Science.

Approved by:


Professor S. Radziszowski


Professor P. Anderson


Professor A. Kitchen


Professor E. Hemaspaandra

December 17, 1998

Abstract:

The purpose of this thesis is to study the behavior of the Hu-Tucker algorithm for building Optimal Alphabetic Binary Search Trees (OABST), to design an efficient implementation, and to evaluate the performance of the algorithm, and the implementation.

The three phases of the algorithm are described and their time complexities evaluated. Two separate implementations for the most expensive phase, Combination, are presented achieving O(n²) and $O(n\lg n)$ time and O(n) space complexity. The break even point between them is experimentally established and the complexities of the implementations are compared against their theoretical time complexities.

The electronic version of ``The Complete Works of William Shakespeare'' is compressed using the Hu-Tucker algorithm and other popular compression algorithms to compare the performance of the different techniques.

The experiments justified the price that has to be paid to implement the Hu-Tucker algorithm. It is shown that an efficient implementation can process extremely large data sets relatively fast and can achieve optimality close to the Optimal Binary Tree, built using the Huffman algorithm, however the OABST can be used in both encoding and decoding processes, unlike the OBT where an additional mapping mechanism is needed for the decoding phase.