The Moving Firefighter Problem

The original formulation of the firefighter problem defines a discrete-time process where a fire starts at a designated subset of the vertices of a graph G. At each subsequent discrete time unit, the fire propagates from each burnt vertex to all of its neighbors unless they are defended by a firefig...

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Vydané v:Mathematics (Basel) Ročník 11; číslo 1; s. 179
Hlavní autori: Gutiérrez-De-La-Paz, Bruno R., García-Díaz, Jesús, Menchaca-Méndez, Rolando, Montenegro-Meza, Mauro A., Menchaca-Méndez, Ricardo, Gutiérrez-De-La-Paz, Omar A.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.01.2023
Predmet:
Algorithms
Analysis
Apexes
Approximation
exact algorithm
Fire extinction
firefighter problem
Firefighters
Forest & brush fires
Graph theory
Graphs
Integer programming
Linear programming
Management
mathematical programming
Methods
Mixed integer
mixed-integer quadratically constrained programming (MIQCP)
np-hard
Optimization
Position (location)
Quadratic functions
spread and containment in networks
Tests, problems and exercises
Time functions
Traveling salesman problem
Wildfires
Mexico
ISSN:2227-7390, 2227-7390
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Shrnutí:The original formulation of the firefighter problem defines a discrete-time process where a fire starts at a designated subset of the vertices of a graph G. At each subsequent discrete time unit, the fire propagates from each burnt vertex to all of its neighbors unless they are defended by a firefighter that can move between any pair of vertices in a single time unit. Once a vertex is burnt or defended, it remains in that state, and the process terminates when the fire can no longer spread. In this work, we present the moving firefighter problem, which is a generalization of the firefighter problem where the time it takes a firefighter to move from a vertex u to defend vertex v is determined by a function τ. This new formulation models situations such as a wildfire or a flood, where firefighters have to physically move from their current position to the location of an entity they intend to defend. It also incorporates the notion that entities modeled by the vertices are not necessarily instantaneously defended upon the arrival of a firefighter. We present a mixed-integer quadratically constrained program (MIQCP) for the optimization version of the moving firefighter problem that minimizes the number of burnt vertices for the case of general finite graphs, an arbitrary set F⊂V of vertices where the fire breaks out, a single firefighter, and metric time functions τ.
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content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math11010179