Computing a Tree Having a Small Vertex Cover

@article{Fukunaga2016ComputingAT,
  title={Computing a Tree Having a Small Vertex Cover},
  author={Takuro Fukunaga and Takanori Maehara},
  journal={ArXiv},
  year={2016},
  volume={abs/1701.08897}
}
In this paper, we consider a new Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an \(O(\log n)\)-approximation algorithm in general graphs with n vertices. This approximation factor is tight because it is known to be NP-hard to achieve an \(o(\log n… 
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On the Parameterized Complexity of Spanning Trees with Small Vertex Covers
TLDR
It is shown that MPST is W,[1]-hard when parameterized by the vertex cover of the input graph, and is W[2]- hard when parameterizing by the solution size—the latter holds even in the case of unit demands.

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