Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Structural and algorithmic aspects of massive social networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fire containment in grids of dimension three and higher
Discrete Applied Mathematics
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Discrete Applied Mathematics
Resource minimization for fire containment
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Surviving Rate of a Graph for the Firefighter Problem
SIAM Journal on Discrete Mathematics
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Cut problems in graphs with a budget constraint
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Better vaccination strategies for better people
Proceedings of the 11th ACM conference on Electronic commerce
Resource minimization for fire containment
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of the firefighter problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Making life easier for firefighters
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Guard your connections: infiltration of a trust/reputation based network
Proceedings of the 3rd Annual ACM Web Science Conference
The firefighter problem with more than one firefighter on trees
Discrete Applied Mathematics
Towards more efficient infection and fire fighting
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Towards more efficient infection and fire fighting
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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We provide approximation algorithms for several variants of the Firefighter problem on general graphs. The Firefighter problem models the case where an infection or another diffusive process (such as an idea, a computer virus, or a fire) is spreading through a network, and our goal is to stop this infection by using targeted vaccinations. Specifically, we are allowed to vaccinate at most B nodes per time-step (for some budget B), with the goal of minimizing the effect of the infection. The difficulty of this problem comes from its temporal component, since we must choose nodes to vaccinate at every time-step while the infection is spreading through the network, leading to notions of "cuts over time".We consider two versions of the Firefighter problem: a "non-spreading" model, where vaccinating a node means only that this node cannot be infected; and a "spreading" model where the vaccination itself is an infectious process, such as in the case where the infection is a harmful idea, and the vaccine to it is another infectious idea. We give complexity and approximation results for problems on both models.