TY - JOUR
T1 - 3/2 firefighters are not enough
AU - Feldheim, Ohad N.
AU - Hod, Rani
N1 - Funding Information:
The research was supported by an ERC advanced grant.
PY - 2013/1
Y1 - 2013/1
N2 - 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.
AB - 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.
KW - Cartesian grid
KW - Firefighting
KW - Infinite graph
KW - Strong grid
UR - http://www.scopus.com/inward/record.url?scp=84869087146&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2012.08.005
DO - 10.1016/j.dam.2012.08.005
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84869087146
SN - 0166-218X
VL - 161
SP - 301
EP - 306
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1-2
ER -