Date of Submission

Spring 2014

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Amir Barghi

Abstract/Artist's Statement

The Firefighter Problem, introduced by Bert Hartnell in 1995, discusses methods of using firefighters to contain of fires on grids. The fire breaks out at a vertex, and a fixed number of firefighters are dispatched to protect endangered vertices from the fire. At each successive time step, the fire spreads from burning vertices to any adjacent vertex not protected by a firefighter. This project attempts to find the minimum number of firefighters needed per time step in order to contain a fire. We look at various types of layered, infinite graphs and use periodic sequences of firefighters to stop fires. Our results build on prior research into periodic firefighting on various single layered graphs. This project shows that the number of firefighters necessary to contain a fire on a graph with multiple layers can be less than that which is needed to contain a fire on a single layered graph.

Open Access Agreement

On-Campus only

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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