3/2 firefighters are not enough

Ohad N. Feldheim; Rani Hod

doi:10.1016/j.dam.2012.08.005

3/2 firefighters are not enough

Ohad N. Feldheim, Rani Hod

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

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 vertices to their unprotected neighbors. In every round, a small amount of unburnt vertices can be protected by firefighters. How many firefighters per turn, on average, are needed to stop the fire from advancing? We prove tight lower and upper bounds on the amount of firefighters needed to control a fire in the Cartesian planar grid and in the strong planar grid, resolving two conjectures of Ng and Raff.

Original language	English
Pages (from-to)	301-306
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	161
Issue number	1-2
DOIs	https://doi.org/10.1016/j.dam.2012.08.005
State	Published - Jan 2013
Externally published	Yes

Bibliographical note

Funding Information:
The research was supported by an ERC advanced grant.

Funding

The research was supported by an ERC advanced grant.

Funders	Funder number
Seventh Framework Programme	226718
European Commission

Keywords

Cartesian grid
Firefighting
Infinite graph
Strong grid

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.dam.2012.08.005

Cite this

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3/2 firefighters are not enough

Abstract

Bibliographical note

Funding

Keywords

UN SDGs

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