Parameterized Complexity of Secluded Connectivity Problems

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...

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Veröffentlicht in:Theory of computing systems Jg. 61; H. 3; S. 795 - 819
Hauptverfasser: Fomin, Fedor V., Golovach, Petr A., Karpov, Nikolay, Kulikov, Alexander S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2017
Springer Nature B.V
Schlagworte:
Complexity
Computer Science
Decision trees
Exposure
Graphs
Parameterization
Shortest-path problems
Terminals
Theory of Computation
Secluded Steiner tree
Parameterized complexity
Secluded path
Kernelization
ISSN:1432-4350, 1433-0490
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-016-9717-x