Politician’s Firefighting

Scott, Allan; Stege, Ulrike; Zeh, Norbert

doi:10.1007/11940128_61

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…Anshelevich et al (2012) introduced different graph models for disease spreading along with approximability analyses. Scott et al (2006) discussed the so-called politician's firefighting problem (PFP). The main difference to the original FFP lies in the fact that the number of firefighters available changes dynamically, as each of the burned vertices creates a new firefighter that can be used to protect one of its untouched neighbors in the next iteration.…”

Section: Literature Reviewmentioning

confidence: 99%

A matheuristic for the firefighter problem on graphs

Ramos

Souza

Rezende

2019

Int Trans Operational Res

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In this paper, we describe a computational study conducted on The Firefighter Problem (FFP), which models fire spreading and containment in a graph. Once the fire breaks out on a set of vertices, the goal is to save as many vertices as possible with limited resources. Practical applications of the FFP occur in areas such as disease control and network security. The FFP is NP‐hard and heuristics have been proposed earlier. Our main contributions include improvements to an existing integer linear programming formulation that led to an average speedup of two to compute exact solutions. Moreover, we developed a novel matheuristic, a technique based on the interoperation between metaheuristics and mathematical programming. We performed extensive experiments on public benchmarks both for parameter tuning and for comparison of our results with those from the literature. A rigorous statistical analysis shows that our new matheuristic outperforms the existing approaches.

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Section: Literature Reviewmentioning

confidence: 99%

A matheuristic for the firefighter problem on graphs

Ramos

Souza

Rezende

2019

Int Trans Operational Res

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“…Modeling a spreading process in a network is a widely studied topic and often relies on a graph theoretical approach (see [4,6,8,12,15,16]). Such processes occur for instance in epidemiology and social sciences.…”

Section: Introductionmentioning

confidence: 99%

The firefighter problem with more than one firefighter on trees

Bazgan

Chopin

Ries

2013

Discrete Applied Mathematics

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In this paper we study the complexity of the firefighter problem and related problems on trees when more than one firefighter is available at each time step, and answer several open questions of [8]. More precisely, when b ≥ 2 firefighters are allowed at each time step, the problem is NP-complete for trees of maximum degree b + 2 and polynomial-time solvable for trees of maximum degree b + 2 when the fire breaks out at a vertex of degree at most b + 1. Moreover we present a polynomial-time algorithm for a subclass of trees, namely k-caterpillars.

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Continuous Firefighting on Infinite Square Grids

Chen

Wang

et al. 2017

Lecture Notes in Computer Science

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Politician’s Firefighting

Cited by 5 publications

References 3 publications

A matheuristic for the firefighter problem on graphs

A matheuristic for the firefighter problem on graphs

The firefighter problem with more than one firefighter on trees

Continuous Firefighting on Infinite Square Grids

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