Surviving rate of graphs and Firefighter Problem

The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion, fire, rumor, computer virus, etc. The fire breaks out at one or more vertices in a graph at the first round, and the firefighter chooses some vertices to protect. The fire spreads to all non-protected...

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Bibliographic Details
Published inFrontiers of Mathematics Vol. 17; no. 2; pp. 227 - 254
Main Authors Wang, Weifan, Kong, Jiangxu
Format Journal Article
LanguageEnglish
Published Beijing Higher Education Press 01.04.2022
Springer Nature B.V
Subjects
Algorithms
Apexes
Burning rate
Computer viruses
Firefighters
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Survey Article
Graph
Firefighter Problem
05C90
surviving rate
burning number
05C57
network
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Summary:The Firefighter Problem on a graph can be viewed as a simplified model of the spread of contagion, fire, rumor, computer virus, etc. The fire breaks out at one or more vertices in a graph at the first round, and the firefighter chooses some vertices to protect. The fire spreads to all non-protected neighbors at the beginning of each time-step. The process stops when the fire can no longer spread. The Firefighter Problem has attracted considerable attention since it was introduced in 1995. In this paper we provide a survey on recent research progress of this field, including algorithms and complexity, Firefighter Problem for special graphs (finite and infinite) and digraphs, surviving rate and burning number of graphs. We also collect some open problems and possible research subjects.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1673-3452
2731-8648
1673-3576
2731-8656
DOI:10.1007/s11464-022-1009-y