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Towards more efficient infection and fire fighting

In English

Författare

Summary, in English

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.

Avdelning/ar

Publiceringsår

2013

Språk

Engelska

Sidor

3-14

Publikation/Tidskrift/Serie

International Journal of Foundations of Computer Science

Volym

24

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

World Scientific Publishing

Ämne

  • Computer Science
  • Mathematics

Nyckelord

  • Approximation algorithms
  • subexponential algorithms

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0129-0541