Toward a Containment Strategy for Smallpox Bioterror: An Individual-Based Computational Approach
Toward a Containment Strategy for Smallpox Bioterror: An Individual-Based Computational Approach
A generalization of the firefighter problem on z × z
Discrete Applied Mathematics
Approximation Algorithms for the Firefighter Problem: Cuts over Time and Submodularity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The surviving rate of an infected network
Theoretical Computer Science
Resource minimization for fire containment
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Surviving Rate of a Graph for the Firefighter Problem
SIAM Journal on Discrete Mathematics
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
SIAM Journal on Discrete Mathematics
Fighting constrained fires in graphs
Theoretical Computer Science
Note: 3/2 firefighters are not enough
Discrete Applied Mathematics
The firefighter problem with more than one firefighter on trees
Discrete Applied Mathematics
Discrete Applied Mathematics
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We consider a deterministic discrete-time model of fire spread introduced by Hartnell [Firefighter! an application of domination, Presentation, in: 20th Conference on Numerical Mathematics and Computing, University of Manitoba in Winnipeg, Canada, September 1995] and the problem of minimizing the number of burnt vertices when a fixed number of vertices can be defended by firefighters per time step. While only two firefighters per time step are needed in the two-dimensional lattice to contain any outbreak, we prove a conjecture of Wang and Moeller [Fire control on graphs, J. Combin. Math. Combin. Comput. 41 (2002) 19-34] that 2d-1 firefighters per time step are needed to contain a fire outbreak starting at a single vertex in the d-dimensional square lattice for d=3; we also prove that in the d-dimensional lattice, d=3, for each positive integer f there is some outbreak of fire such that f firefighters per time step are insufficient to contain the outbreak. We prove another conjecture of Wang and Moeller that the proportion of elements in the three-dimensional grid P"nxP"nxP"n which can be saved with one firefighter per time step when an outbreak starts at one vertex goes to 0 as n gets large. Finally, we use integer programming to prove results about the minimum number of time steps needed and minimum number of burnt vertices when containing a fire outbreak in the two-dimensional square lattice with two firefighters per time step.