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TOWARDS MORE EFFICIENT INFECTION AND FIRE FIGHTING.

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Title: TOWARDS MORE EFFICIENT INFECTION AND FIRE FIGHTING.
Authors: FLODERUS, PETER1 pflo@maths.Ith.se, LINGAS, ANDRZEJ2 Andrzej.Lingas@cs.Ith.se, PERSSON, MIA3 mia.persson@mah.se
Source: International Journal of Foundations of Computer Science. Jan2013, Vol. 24 Issue 1, p3-14. 12p. 3 Diagrams.
Subjects: Algorithms, Firefighting, Computer viruses, Vaccination, Graph theory, Mathematical models, Approximation theory, Computational complexity
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(l). In a non-standard 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 20(√n log n) -time algorithm. In the special case of trees, where the standard and spreading model are equivalent, our algorithm is substan-tially 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 C DTIME (nO(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 firefighter problem for the so called directed layered graphs. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Foundations of Computer Science is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 88128751
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: TOWARDS MORE EFFICIENT INFECTION AND FIRE FIGHTING.
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  Data: <searchLink fieldCode="AR" term="%22FLODERUS%2C+PETER%22">FLODERUS, PETER</searchLink><relatesTo>1</relatesTo><i> pflo@maths.Ith.se</i><br /><searchLink fieldCode="AR" term="%22LINGAS%2C+ANDRZEJ%22">LINGAS, ANDRZEJ</searchLink><relatesTo>2</relatesTo><i> Andrzej.Lingas@cs.Ith.se</i><br /><searchLink fieldCode="AR" term="%22PERSSON%2C+MIA%22">PERSSON, MIA</searchLink><relatesTo>3</relatesTo><i> mia.persson@mah.se</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Foundations+of+Computer+Science%22">International Journal of Foundations of Computer Science</searchLink>. Jan2013, Vol. 24 Issue 1, p3-14. 12p. 3 Diagrams.
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  Data: <searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Firefighting%22">Firefighting</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+viruses%22">Computer viruses</searchLink><br /><searchLink fieldCode="DE" term="%22Vaccination%22">Vaccination</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink>
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  Label: Abstract
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  Data: 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(l). In a non-standard 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 20(√n log n) -time algorithm. In the special case of trees, where the standard and spreading model are equivalent, our algorithm is substan-tially 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 C DTIME (nO(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 firefighter problem for the so called directed layered graphs. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Foundations of Computer Science is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1142/S0129054113400017
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 3
    Subjects:
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Firefighting
        Type: general
      – SubjectFull: Computer viruses
        Type: general
      – SubjectFull: Vaccination
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Approximation theory
        Type: general
      – SubjectFull: Computational complexity
        Type: general
    Titles:
      – TitleFull: TOWARDS MORE EFFICIENT INFECTION AND FIRE FIGHTING.
        Type: main
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            NameFull: FLODERUS, PETER
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            NameFull: LINGAS, ANDRZEJ
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            NameFull: PERSSON, MIA
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            – D: 01
              M: 01
              Text: Jan2013
              Type: published
              Y: 2013
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