Computing a Tree Having a Small Vertex Cover
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- Fukunaga T., Maehara T. (2016) Computing a Tree Having a Small Vertex Cover. In: Chan TH., Li M., Wang L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science, vol 10043. Springer, Cham
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 \(o(\log n)\)-approximation for the problem with general graphs. In this paper, we present constant-factor approximation algorithms for the problem with unit disk graphs and with graphs excluding a fixed minor.