Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover

Fast Fixed-Parameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover

Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class Wk(G), where for each graph G in Wk(G), the removal of a set of at most k vertices from...

Exact Algorithms for Generalizations of Vertex Cover

The NP-complete Vertex Cover problem has been intensively studied in the field of parameterized complexity theory. However, there exists only little work concerning important generalizations of Vertex Cover like Partial Vertex Cover, Connected Vertex Cover, and Capacitated Vertex Cover which are of high interest in theory as well as in real-world applications. So far research was mainly focused...

On Efficient Fixed Parameter Algorithms for WEIGHTED VERTEX COVER

We investigate the fixed parameter complexity of one of the most popular problems in combinatorial optimization, Weighted Vertex Cover. Given a graph G = (V, E), a weight function ω : V → R, and k ∈ R, Weighted Vertex Cover (WVC for short) asks for a subset C of vertices in V of weight at most k such that every edge of G has at least one endpoint in C. WVC and its variants have all been shown t...

Towards Fixed-Parameter Tractable Algorithms for Argumentation

Abstract argumentation frameworks have received a lot of interest in recent years. Most computational problems in this area are intractable but several tractable fragments have been identified. In particular, Dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree-width. However, these tractability results, which were obtained via Courcelle’s Th...

Solving Minimum Vertex Cover : A Fast Fixed - Parameter - Tra table Algorithm for Pro t Cover ?