Related papers: Parameterized Complexity of Firefighting Revisited
The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…
The firefighter problem is defined as below. A fire initially breaks out at a vertex r on a graph G. In each step, a firefighter chooses to protect one vertex, which is not yet burnt. And the fire spreads out to its unprotected neighboring…
We consider the problem of firefighting to save a critical subset of nodes. The firefighting game is a turn-based game played on a graph, where the fire spreads to vertices in a breadth-first manner from a source, and firefighters can be…
It is well known that fighting a fire is a hard task. The Firefighter problem asks how to optimally deploy firefighters to defend the vertices of a graph from a fire. This problem is NP-Complete on all but a few classes of graphs.…
We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of…
We investigate a new oriented variant of the Firefighter Problem. In the traditional Firefighter Problem, a fire breaks out at a given vertex of a graph, and at each time interval spreads to neighbouring vertices that have not been…
The Firefighter Problem (FP) is a graph problem originally introduced in 1995 to model the spread of a fire in a graph, which has attracted considerable attention in the literature. The goal is to devise a strategy to employ a given…
The firefighter problem with $k$ firefighters on an infinite graph $G$ is an iterative graph process, defined as follows: Suppose a fire breaks out at a given vertex $v\in V(G)$ on Turn 1. On each subsequent even turn, $k$ firefighters…
In the Firefighter problem, introduced by Hartnell in 1995, a fire spreads through a graph while a player chooses which vertices to protect in order to contain it. In this paper, we focus on the case of trees and we consider as well the…
In this paper, we consider the \emph{firefighter problem} on a graph $G=(V,E)$ that is either finite or infinite. Suppose that a fire breaks out at a given vertex $v \in V$. In each subsequent time unit, a firefighter protects one vertex…
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph $G$ and then $b$ firefighters protect $b$ vertices. On each subsequent turn, the fire spreads to the collective unburned…
The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning…
We consider a pursuit-evasion game that describes the process of extinguishing a fire burning on the nodes of an undirected graph. We denote the minimum number of firefighters required by ffn(G) and provide almost sharp bounds to this graph…
Consider a model of fire spreading through a graph; initially some vertices are burning, and at every given time-step fire spreads from burning vertices to their neighbours. The firefighter problem is a solitaire game in which a player is…
The Firefighter problem and a variant of it, known as Resource Minimization for Fire Containment (RMFC), are natural models for optimal inhibition of harmful spreading processes. Despite considerable progress on several fronts, the…
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 Finbow and MacGillivray 2009. More precisely,…
In this paper, we consider the following \emph{$k$-many firefighter problem} on a finite graph $G=(V,E)$. Suppose that a fire breaks out at a given vertex $v \in V$. In each subsequent time unit, a firefighter protects $k$ vertices which…
The firefighter game problem on locally finite connected graphs was introduced by Bert Hartnell. The game on a graph $G$ can be described as follows: let $f_n$ be a sequence of positive integers; an initial fire starts at a finite set of…
Unit disk graphs are the set of graphs which represent the intersection of disk graphs and interval graphs. These graphs are of great importance due to their structural similarity with wireless communication networks. Firefighter problem on…
A set S of vertices of a graph is a defensive alliance if, for each element of S, the majority of its neighbors is in S. The problem of finding a defensive alliance of minimum size in a given graph is NP-hard and there are polynomial-time…