Results 101 to 110 of about 1,231 (135)
The firefighter problem with more than one firefighter on trees
Discrete Applied Mathematics, 2013 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, when $b \geq 2$ firefighters are allowed at each time step, the problem is NP-complete for trees of maximum ...
Cristina Bazgan +2 more
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The firefighter problem for cubic graphs
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gary Macgillivray
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The Firefighter problem on graph classes
Theoretical Computer Science, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fedor V Fomin +2 more
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The Surviving Rate of a Graph for the Firefighter Problem [PDF]
SIAM Journal on Discrete Mathematics, 2010 Summary: We consider the following firefighter problem on a graph \(G=(V,E)\). Initially, a fire breaks out at a vertex \(v\) of \(G\). In each subsequent time unit, a firefighter protects one vertex, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as possible.
Cai Leizhen
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Surviving rate of graphs and Firefighter Problem
Frontiers of Mathematics in China, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weifan Wang, Jiangxu Kong
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Improved Approximation Algorithms for Firefighter Problem on Trees
IEICE Transactions on Information and Systems, 2011 The firefighter problem is used to model the spread of fire, infectious diseases, and computer viruses. This paper deals with firefighter problem on rooted trees. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. We propose techniques to improve a given approximation algorithm.
Naoyuki Kamiyama, Tomomi Matsui
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The firefighter problem on polynomial and intermediate growth groups [PDF]
Discrete Mathematics, 2020 We prove that any Cayley graph $G$ with degree $d$ polynomial growth does not satisfy $\{f(n)\}$-containment for any $f=o(n^{d-2})$. This settles the asymptotic behaviour of the firefighter problem on such graphs as it was known that $Cn^{d-2}$ firefighters are enough, answering and strengthening a conjecture of Develin and Hartke.
Gideon Amir +2 more
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The surviving rate of an outerplanar graph for the firefighter problem
Theoretical Computer Science, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weifan Wang
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A matheuristic for the firefighter problem on graphs
International Transactions in Operational Research, 2019AbstractIn 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.
Natanael Ramos +2 more
openaire +1 more source