Parameterized Complexity of Generalized Vertex Cover Problems

Abstract

AbstractImportant generalizations of the Vertex Cover problem (Connected Vertex Cover, Capacitated Vertex Cover, and Maximum Partial Vertex Cover) have been intensively studied in terms of approximability. However, their parameterized complexity has so far been completely open. We close this gap here by showing that, with the size of the desired vertex cover as parameter, Connected Vertex Cover and Capacitated Vertex Cover are both fixed-parameter tractable while Maximum Partial Vertex Cover is W[1]-hard. This answers two open questions from the literature. The results extend to several closely related problems. Interestingly, although the considered generalized Vertex Cover problems behave very similar in terms of constant-factor approximability, they display a wide range of different characteristics when investigating their parameterized complexities.KeywordsTree CoverSteiner TreeParameterized ComplexityVertex CoverMinimal VertexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.