3/2 firefighters are not enough

Ohad N. Feldheim, Rani Hod

Research output: Contribution to journalArticlepeer-review

17 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 languageEnglish (US)
Pages (from-to)301-306
Number of pages6
JournalDiscrete Applied Mathematics
Volume161
Issue number1-2
DOIs
StatePublished - Jan 2013

Bibliographical note

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

Keywords

  • Cartesian grid
  • Firefighting
  • Infinite graph
  • Strong grid

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