Sequential optimization of binary search trees for multiple cost functions

Authors:
Maram Alnafie;Igor Chikalov;Shahid Hussain;Mikhail Moshkov
Affiliations:
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Venue:
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Year:
2011

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Abstract

In this paper, we present a methodology to model the optimal binary search tree problem as a directed acyclic graph to extract all possible optimal solutions. We provide a mechanism to find optimal binary search trees relative to different types of cost functions, sequentially. We prove that for a set of n keys our optimization procedure makes O(n3) arithmetic operations per cost function such as weighted depth or average weighted depth.