Probabilistic Firefighting
| dc.contributor.author | Pearson, Dylan | |
| dc.contributor.copyright-release | Not Applicable | |
| dc.contributor.degree | Master of Science | |
| dc.contributor.department | Department of Mathematics & Statistics - Math Division | |
| dc.contributor.ethics-approval | Not Applicable | |
| dc.contributor.external-examiner | n/a | |
| dc.contributor.manuscripts | Not Applicable | |
| dc.contributor.thesis-reader | Jason Brown | |
| dc.contributor.thesis-reader | Margaret-Ellen Messinger | |
| dc.contributor.thesis-supervisor | Jeannette Janssen | |
| dc.contributor.thesis-supervisor | Nancy Clarke | |
| dc.date.accessioned | 2024-12-16T13:30:51Z | |
| dc.date.available | 2024-12-16T13:30:51Z | |
| dc.date.defence | 2024-12-10 | |
| dc.date.issued | 2024-12-14 | |
| dc.description | In this thesis, we study a model for the spread of, and defense against, a wildfire. Prior work in this field has considered the spread of a fire to occur deterministically. However, variables like wind, humidity, temperature and precipitation are all important factors that dictate how a fire disseminates. To account for this, we assign a probability to the spread of the fire. In doing so, we are able to explore new strategies to fight fires that were previously impossible via other models. | |
| dc.description.abstract | Firefighting is a model used to study the spread of a fire on a graph G over discrete time-steps. Initially, a fire breaks out at some vertex of G. At each successive step , a firefighter defends an unburned vertex, and then the fire spreads to each unburned, undefended neighbour. The process terminates once the fire is stopped from spreading to any new vertices. We introduce probabilistic firefighting, where the fire only spreads to neighbours with a fixed probability. In this model, we say that the fire is contained if the probability that any new vertices burn is 0. We study strategies to contain a probabilistic fire on the kth power of a path and on the hexagonal grid. We conjecture that a probabilistic fire can be contained with one firefighter on the hexagonal grid, providing new insight into Messinger’s conjecture. | |
| dc.identifier.uri | https://hdl.handle.net/10222/84787 | |
| dc.language.iso | en | |
| dc.subject | Graph Theory | |
| dc.subject | Firefighting | |
| dc.subject | Probability | |
| dc.title | Probabilistic Firefighting |