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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.

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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.

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

- Mathematics, Computer ScienceArXiv
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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 ScienceArXiv
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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 ScienceISAAC
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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.

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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.

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