Undergraduate Honors Thesis Projects

Date of Award

Spring 2020

Document Type

Honors Paper

Degree Name

Mathematics-BS

Department

Mathematical Sciences

Advisor

David Stucki

First Committee Member

David Stucki

Second Committee Member

Pei Pei

Third Committee Member

Erica Van Drop

Keywords

Randomized Algorithms, Monte Carlo Algorithm, Las Vegas Algorithm, Hashing and Pseudo Random Number Generators

Subject Categories

Mathematics | Theory and Algorithms

Abstract

Randomness is an interesting and very beneficial phenomenon. In computer science randomness facilitates great advances in efficiency but topics like randomized algorithms aren’t taught until someone enters graduate school. This paper provides undergraduates as well as people unacquainted with computer science an opportunity to explore the topic of randomness by guiding them from essential topics all the way through the graduate level topic of randomized algorithms. Topics like what an algorithm is, how they are represented and the history that brought them into existence bring the reader up to speed before diving deeper into randomized algorithms. A discussion of complexity theory is used to motivate the reader as to why randomized algorithms are so important and beneficial. Then the remainder of the paper is used to describe the categorization of randomized algorithm by goal as well as some of the applications of randomized algorithms including hashing, random sampling and generating random numbers. The paper concludes with a discussion of a real-world application of randomized algorithms, the Kidney Exchange Problem, where incompatible patient-donor pairs are matched with others to facilitate successful kidney transplants.

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