Towards more efficient infection and fire fighting
(2013) In International Journal of Foundations of Computer Science 24(1). p.314 Abstract
 The firefighter problem models the situation where an infection, a computer virus, an idea or fire etc. is spreading through a network and the goal is to save as many as possible nodes of the network through targeted vaccinations. The number of nodes that can be vaccinated at a single timestep is typically one, or more generally O(1). In a nonstandard model, the so called spreading model, the vaccinations also spread in contrast to the standard model. Our main results are concerned with general graphs in the spreading model. We provide a very simple exact 2(O(root n log n))time algorithm. In the special case of trees, where the standard and spreading model are equivalent, our algorithm is substantially simpler than that exact... (More)
 The firefighter problem models the situation where an infection, a computer virus, an idea or fire etc. is spreading through a network and the goal is to save as many as possible nodes of the network through targeted vaccinations. The number of nodes that can be vaccinated at a single timestep is typically one, or more generally O(1). In a nonstandard model, the so called spreading model, the vaccinations also spread in contrast to the standard model. Our main results are concerned with general graphs in the spreading model. We provide a very simple exact 2(O(root n log n))time algorithm. In the special case of trees, where the standard and spreading model are equivalent, our algorithm is substantially simpler than that exact subexponential algorithm for trees presented in Ref. 2. On the other hand, we show that the firefighter problem on weighted directed graphs in the spreading model cannot be approximated within a constant factor better than 1  1/e unless NP subset of DTIME (n(O(log log n))) We also present several results in the standard model. We provide approximation algorithms for planar graphs in case when at least two vaccinations can be performed at a timestep. We also derive tradeoffs between approximation factors for polynomialtime solutions and the time complexity of exact or nearly exact solutions for instances of the fireifighter problem for the so called directed layered graphs. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3932340
 author
 Floderus, Peter ^{LU} ; Lingas, Andrzej ^{LU} and Persson, Mia ^{LU}
 organization
 publishing date
 2013
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Approximation algorithms, subexponential algorithms
 in
 International Journal of Foundations of Computer Science
 volume
 24
 issue
 1
 pages
 3  14
 publisher
 World Scientific
 external identifiers

 wos:000319124000002
 scopus:84877953705
 ISSN
 01290541
 DOI
 10.1142/S0129054113400017
 language
 English
 LU publication?
 yes
 id
 8656da1727ec4e7e83441b1e649e4da8 (old id 3932340)
 date added to LUP
 20160401 10:57:47
 date last changed
 20200115 02:04:29
@article{8656da1727ec4e7e83441b1e649e4da8, abstract = {The firefighter problem models the situation where an infection, a computer virus, an idea or fire etc. is spreading through a network and the goal is to save as many as possible nodes of the network through targeted vaccinations. The number of nodes that can be vaccinated at a single timestep is typically one, or more generally O(1). In a nonstandard model, the so called spreading model, the vaccinations also spread in contrast to the standard model. Our main results are concerned with general graphs in the spreading model. We provide a very simple exact 2(O(root n log n))time algorithm. In the special case of trees, where the standard and spreading model are equivalent, our algorithm is substantially simpler than that exact subexponential algorithm for trees presented in Ref. 2. On the other hand, we show that the firefighter problem on weighted directed graphs in the spreading model cannot be approximated within a constant factor better than 1  1/e unless NP subset of DTIME (n(O(log log n))) We also present several results in the standard model. We provide approximation algorithms for planar graphs in case when at least two vaccinations can be performed at a timestep. We also derive tradeoffs between approximation factors for polynomialtime solutions and the time complexity of exact or nearly exact solutions for instances of the fireifighter problem for the so called directed layered graphs.}, author = {Floderus, Peter and Lingas, Andrzej and Persson, Mia}, issn = {01290541}, language = {eng}, number = {1}, pages = {314}, publisher = {World Scientific}, series = {International Journal of Foundations of Computer Science}, title = {Towards more efficient infection and fire fighting}, url = {http://dx.doi.org/10.1142/S0129054113400017}, doi = {10.1142/S0129054113400017}, volume = {24}, year = {2013}, }