Extended Spanning Star Forest Problems

We continue the investigation proposed in [COCOA 2016, Weller, Chateau, Giroudeau, König and Pollet “On Residual Approximation in Solution Extension Problems”] about the study of extended problems. In this context, a partial feasible solution is given in advance and the goal is to extend this partial solution. In this paper, we focus on the edge-weighted spanning star forest problem for both minimization and maximization versions. The goal here is to find a vertex partition of an edge-weighted complete graph into disjoint non-trivial stars and the value of a solution is given by the sum of the edge-weights of the stars. We propose NP-hardness, parameterized complexity, positive and negative approximation results.