# Fire containment in grids of dimension three and higher

@article{Develin2007FireCI,
title={Fire containment in grids of dimension three and higher},
author={Mike Develin and Stephen G. Hartke},
journal={Discret. Appl. Math.},
year={2007},
volume={155},
pages={2257-2268}
}
• Published 13 September 2004
• Computer Science
• Discret. Appl. Math.

## Figures from this paper

Continuous Firefighting on Infinite Square Grids
• Environmental Science
TAMC
• 2017
The classical firefighter problem, introduced by Bert Hartnell in 1995, is a deterministic discrete-time model of the spread and defence of fire, rumor, or disease, and the continuous firefighting model is proposed.
Firefighting as a Strategic Game
• Computer Science
Internet Math.
• 2016
A strategic game model for the Firefighter Problem is introduced to tackle its complexity from a different angle and it turns out that it is possible to compute an equilibrium in polynomial time, even for constant-size coalitions.
Fighting constrained fires in graphs
• Mathematics
Theor. Comput. Sci.
• 2012
Firefighting as a Strategic Game ∗ † Carme
• Computer Science
• 2015
The Firefighter Problem was proposed in 1995 [25] as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V,E),
Fixed Parameter Tractable Algorithm for Firefighting Problem
This paper introduces a parameter k into the firefighter problem and gives several FPT algorithms using a random separation technique of Cai, Chan and Chan and parameterize the number of protected vertices to take total number of vertices burnt to be a parameter.
The Stochastic Firefighter Problem
• Computer Science
ArXiv
• 2017
This work extends the Firefighter problem to a probabilistic setting, where the infection is stochastic, and devise a simple policy that only vaccinates neighbors of infected nodes and is optimal on regular trees and on general graphs for a sufficiently large budget.
Firefighting on Trees: (1-1/e)-Approximation, Fixed Parameter Tractability and a Subexponential Algorithm
• Computer Science
ISAAC
• 2008
A (1 - 1/e)-approximation algorithm based on LP relaxation and randomized rounding, and several FPT algorithms using a random separation technique of Cai, Chan and Chan are presented and an $2^{O(\sqrt{n}\log n)}$-time subexponential algorithm is obtained.
Resource minimization for fire containment
• Computer Science
SODA '10
• 2010
A simple mathematical model abstracting the dynamic nature of fire containment and other natural processes, such as the spread of a perfectly contagious disease and its containment via vaccination, and an O(log n)-approximation LP-rounding algorithm, matching the integrality gap of the LP relaxation are considered.

## References

SHOWING 1-10 OF 12 REFERENCES
Disease evolution on networks: the role of contact structure
• Biology
Proceedings of the Royal Society of London. Series B: Biological Sciences
• 2003
This paper investigates how a disease may adapt in response to the routes of transmission available between infected and susceptible individuals, using a computer–generated contact network to define potential transmission routes.
Chapter 12. TOWARD A CONTAINMENT STRATEGY FOR SMALLPOX BIOTERROR: AN INDIVIDUAL-BASED COMPUTATIONAL APPROACH
• Economics
• 2004
Toward a Containment Strategy for Smallpox Bioterror describes the scientific results and policy implications of a simulation of a smallpox epidemic in a two-town county and the extension of these techniques to the containment of emerging pathogens, such as SARS.
Wang, and the EpiSims Team
• Wang, and the EpiSims Team
• 2004
and the EpiSims Team
• http://episims.lanl.gov, April 22
• 2004
the EpiSims Team
• 〈http://episims.lanl.gov〉, April 22
• 2004
Firefighter! an application of domination, Presentation
• 20th Conference on Numerical Mathematics and Computing
• 1995
Catching the fire on grids
• Catching the fire on grids
• 2003
Firefighter! An Application of Domination, presentation, Twentieth Conference on Numerical Mathematics and Computing, University of Manitoba
• 1995
Fire control on graphs
• J. Combin. Math. Combin. Comput
• 2002
Wang, the EpiSims Team
• Wang, the EpiSims Team
• 2004