Computing a tree having a small vertex cover
Abstract
We consider a new Steiner tree problem, called vertexcoverweighted 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 minimumweight Steiner tree in a given vertexweighted 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 up to a constant because it is NPhard to achieve an o(log n)approximation for the vertexcoverweighted Steiner tree problem on general graphs even if the given vertex weights are uniform and a spanning tree is required instead of a Steiner tree. In this paper, we present constantfactor approximation algorithms for the problem with unit disk graphs and with graphs excluding a fixed minor. For the latter graph class, our algorithm can be also applied for the Steiner tree activation problem.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.08897
 Bibcode:
 2017arXiv170108897F
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 appeared in COCOA 2016