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2010

Parameterized algorithm for eternal vertex cover

8 years 5 months ago
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...
Fedor V. Fomin, Serge Gaspers, Petr A. Golovach, D
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where IPL
Authors Fedor V. Fomin, Serge Gaspers, Petr A. Golovach, Dieter Kratsch, Saket Saurabh
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