Title
A Hike Through the Forest: The Knapsack Problem in Graph Theory
Document Type
Article
Contributor
Eaton, Nancy [faculty advisor, Department of Mathematics]
Date
May 2008
Subject
Mathematics
Format Data
Adobe Acrobat document, 291,699 bytes; Adobe Acrobat document, 43,839 bytes 2008 URI Senior Honors Project
Keywords
graph theory; knapsack; algorithm
Abstract
Graph theory is a branch of mathematics which studies graphs a col-
lection of a set of edges and vertices used to sometimes model structures.
My interest in graph theory began last semester in a math/computer sci-
ence course entitled \Discrete Structures." One aspect which makes graph
theory an appealing area to research is the amount of understanding that
comes from a relatively short amount of time spent learning the subject
material. The visual appeal of being able to draw a graph along practical
applications that surface daily make graph theory a prime candidate for
further research.
Through research of the history of graph theory, reading of research
papers, and manipulation of theorems and de nitions, the importance
of communication within the realm of mathematics is discovered, result-
ing in an appreciation of what math research entails. By learning more
about open graph theory research problems and seeing how many of the
problems, if solved, provide a solution for many other research problems,
the importance of math research, speci cally graph theory research, is
demonstrated.
After deepening knowledge about de nitions of terms, solving home-
work problems and proving theorems, I selected a certain subset of graph
theory, namely the Knapsack combinatorial optimization problem, to try
to create new techniques for obtaining approximations of solutions. Through
experimentation and trial and error, conclusions are drawn about the open
research problem. As a result of performing independent undergraduate
research in graph theory, graduate math research is experienced in prepa-
ration for graduate school, reiterating the importance of verbal and writ-
ten communication of mathematical concepts and ideas while deepening
my mathematical appreciation and understanding of graph theory.
Knapsack Code
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