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Towards more efficient infection and fire fighting

Floderus, Peter LU ; Lingas, Andrzej LU and Persson, Mia LU (2013) In International Journal of Foundations of Computer Science 24(1). p.3-14
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 time-step 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 time-step 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 time-step. We also derive trade-offs between approximation factors for polynomial-time 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:
author
organization
publishing date
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
0129-0541
DOI
10.1142/S0129054113400017
language
English
LU publication?
yes
id
8656da17-27ec-4e7e-8344-1b1e649e4da8 (old id 3932340)
date added to LUP
2016-04-01 10:57:47
date last changed
2020-01-15 02:04:29
@article{8656da17-27ec-4e7e-8344-1b1e649e4da8,
  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 time-step 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 time-step. We also derive trade-offs between approximation factors for polynomial-time 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         = {0129-0541},
  language     = {eng},
  number       = {1},
  pages        = {3--14},
  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},
}