Snow Plow Project

One potential project I have considered deals with optimizing the routes of snow plows in Iowa City to ensure that all streets are cleared of snow in as little time as possible. I suggest this topic because, during the winter of 2007-2008, my area was not plowed for several weeks. I would like to understand the complexity involved in planning these routes to avoid future ire toward the city. I believe we are going to examine a similar problem in class (concerning garbage trucks). Because we have not yet begun this, I am not sure about intensity of the math involved, but I would like to take this example to a large scale. This should include research about which areas fall under the responsibility of Iowa City, how many plows the city can use, and which areas are of higher priority. From this research, and, hopefully, a bit of math, I would make potential hypothetical recommendations to the city. This could involve different routes or even the purchase of more snowplows to optimize effectiveness of the plowing system.

Prey-Predator Model

A second potential project involves examining a proposed alteration to the Beddington-DeAngelis prey-predator model. This involves looking into the relationships between predator and prey, and how their populations can be used to predict the relationship for the following season. An article I have found on this also describes the complexity of each model and how complexity changes based on the elements involved in the model.

Gakkhar, S., Negi, K., & Sahani, S. K. (2009). Effects of seasonal growth on ratio dependent delayed prey predator system. Communications in Nonlinear Science and Numerical Simulation , 850-862.

Graph Theory

A final potential project involves delving deeper into graph theory. I have found several articles concerning proofs regarding graph theory. For example, I found an article which shows the following. For a family of n connected sets in the plane with an intersection graph, G(C), which has no complete bipartite subgraph with k verticies in each of its classes, then it can be shown that this intersection graph G(C) has at most n times a polologarithmic number of edges, where the exponent of the logarithmic factor depends on k. I am very interested in graph theory, as I have no previous experience with it. I would like to further examine some of these proofs.

Pach, J., & Sharir, M. (2008). On Planar Intersection Graphs with Forbidden Subgraphs. Journal of Graph Theory , 205-214.