Parameterized Complexity of Secluded Connectivity Problems

  • Fedor V. Fomin
  • Petr A. Golovach
  • Nikolay Karpov
  • Alexander S. Kulikov
Article

DOI: 10.1007/s00224-016-9717-x

Cite this article as:
Fomin, F.V., Golovach, P.A., Karpov, N. et al. Theory Comput Syst (2016). doi:10.1007/s00224-016-9717-x
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Abstract

The Secluded Path problem models a situation where sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure cost, which is the total cost of vertices in its closed neighborhood. The task is to select a secluded path, i.e., a path with a small exposure cost. Similarly, the Secluded Steiner Tree problem is to find a tree in a graph connecting a given set of terminals such that the exposure cost of the tree is minimized. In this paper we present a systematic study of the parameterized complexity of Secluded Steiner Tree. In particular, we establish the tractability of Secluded Path being parameterized by “above guarantee” value, which in this case is the length of a shortest path between vertices. We also show how to extend this result for Secluded Steiner Tree, in this case we parameterize above the size of an optimal Steiner tree and the number of terminals. We also consider various parameterization of the problems such as by the treewidth, the size of a vertex cover, feedback vertex set, or the maximum vertex degree and establish kernelization complexity of the problem subject to different choices of parameters.

Keywords

Secluded path Secluded Steiner tree Parameterized complexity Kernelization 

Funding information

Funder NameGrant NumberFunding Note
European Research Council
  • 267959
  • 267959
Government of the Russian Federation
  • 14.Z50.31.0030

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Fedor V. Fomin
    • 1
    • 2
  • Petr A. Golovach
    • 1
    • 2
  • Nikolay Karpov
    • 2
  • Alexander S. Kulikov
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Steklov Institute of Mathematics at St. Petersburg, Russian Academy of SciencesSaint PetersburgRussia

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