Optimal binary trees with height restrictions on left and right branches

Identifier

etd-07122006-160111

Author

Song Ding, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

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(n²), while previous algorithms had been O(n³) (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.

Date

2006

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Ding, Song, "Optimal binary trees with height restrictions on left and right branches" (2006). LSU Master's Theses. 3217.
https://repository.lsu.edu/gradschool_theses/3217

Committee Chair

James Madden

DOI

10.31390/gradschool_theses.3217