Improved Approximation Algorithms for the Spanning Star Forest Problem

A star graph is a tree of diameter at most two. A star forest is a graph that consists of node-disjoint star graphs. In the spanning star forest problem, given an unweighted graph G, the objective is to find a star forest that contains all the vertices of G and has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with n vertices, the size of the maximum spanning star forest is equal to n minus the size of the minimum dominating set. We present a 0.71-approximation algorithm for this problem, improving upon the approximation factor of 0.6 of Nguyen et al. [9]. We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Finally, we present improved hardness of approximation results for the weighted versions of the problem.

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Ning Chen, Roee Engelberg, C. Thach Nguyen, Prasad Raghavendra, Atri Rudra, Gyanit Singh
• Keywords: Algorithms, APPROX 2007, Spanning Star Forest, Star Forest, Star Graphs