TY - JOUR

T1 - Parameterized Complexity of Secluded Connectivity Problems

AU - Fomin, Fedor V.

AU - Golovach, Petr A.

AU - Karpov, Nikolay

AU - Kulikov, Alexander S.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Kernelization

KW - Parameterized complexity

KW - Secluded path

KW - Secluded Steiner tree

UR - http://www.scopus.com/inward/record.url?scp=84994442655&partnerID=8YFLogxK

U2 - 10.1007/s00224-016-9717-x

DO - 10.1007/s00224-016-9717-x

M3 - Article

AN - SCOPUS:84994442655

VL - 61

SP - 795

EP - 819

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 3

ER -