Parameterized algorithm for eternal vertex cover

In this paper we initiate the study of a "dynamic" variant of the classical Vertex Cover problem, the Eternal Vertex Cover problem introduced by Klostermeyer and Mynhardt, from the perspective of parameterized algorithms. This problem consists in placing a minimum number of guards on the vertices of a graph such that these guards can protect the graph from any sequence of attacks on its edges. In response to an attack, each guard is allowed either to stay in his vertex, or to move to a neighboring vertex. However, at least one guard has to fix the attacked edge by moving along it. The other guards may move to reconfigure and prepare for the next attack. Thus at every step the vertices occupied by guards form a vertex cover. We show that the problem admits a kernel of size 4k (k + 1) + 2k, which shows that the problem is fixed parameter tractable when parameterized by the number of available guards k. Finally, we also provide an algorithm with running time O(2O(k2 ) + nm) for...

• Type: Journal
• Year: 2010
• Where: IPL
• Authors: Fedor V. Fomin, Serge Gaspers, Petr A. Golovach, Dieter Kratsch, Saket Saurabh
• Keywords: Eternal Vertex Cover, IPL 2010, Medical Imaging, Vertex Cover, Vertex Cover Problem