Optimal Binary Trees with Height Restrictions on Left and Right Branches

We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity...

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Main Author:	Ding, Song
Other Authors:	Jianhua Chen
Format:	Others
Language:	en
Published:	LSU 2006
Subjects:	Mathematics
Online Access:	http://etd.lsu.edu/docs/available/etd-07122006-160111/

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spelling	ndltd-LSU-oai-etd.lsu.edu-etd-07122006-1601112013-01-07T22:50:44Z Optimal Binary Trees with Height Restrictions on Left and Right Branches Ding, Song Mathematics We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n<sup>2</sup>), while previous algorithms had been O(n<sup>3</sup>) (n = size of input). We present the known generalization of Knuth's algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and right heights. We prove the Quadrangle Lemma and the Monoticity Theorem in this case, and present an algorithm based on this. Jianhua Chen Robert Perlis James Madden LSU 2006-07-13 text application/pdf http://etd.lsu.edu/docs/available/etd-07122006-160111/ http://etd.lsu.edu/docs/available/etd-07122006-160111/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.
collection	NDLTD
language	en
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Ding, Song Optimal Binary Trees with Height Restrictions on Left and Right Branches
description	We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n<sup>2</sup>), while previous algorithms had been O(n<sup>3</sup>) (n = size of input). We present the known generalization of Knuth's algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and right heights. We prove the Quadrangle Lemma and the Monoticity Theorem in this case, and present an algorithm based on this.
author2	Jianhua Chen
author_facet	Jianhua Chen Ding, Song
author	Ding, Song
author_sort	Ding, Song
title	Optimal Binary Trees with Height Restrictions on Left and Right Branches
title_short	Optimal Binary Trees with Height Restrictions on Left and Right Branches
title_full	Optimal Binary Trees with Height Restrictions on Left and Right Branches
title_fullStr	Optimal Binary Trees with Height Restrictions on Left and Right Branches
title_full_unstemmed	Optimal Binary Trees with Height Restrictions on Left and Right Branches
title_sort	optimal binary trees with height restrictions on left and right branches
publisher	LSU
publishDate	2006
url	http://etd.lsu.edu/docs/available/etd-07122006-160111/
work_keys_str_mv	AT dingsong optimalbinarytreeswithheightrestrictionsonleftandrightbranches
_version_	1716477386425368576

Optimal Binary Trees with Height Restrictions on Left and Right Branches

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