Ning Chen, Roee Engelberg, Cam Thach Nguyen, Prasad Raghavendra, Atri Rudra and Gyanit Singh

Improved Approximation Algorithms for the Spanning Star Forest Problem

Abstract :

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. We also present a 0.64-approximation algorithm for the problem on node-weighted graphs. Our algorithms use an new non-linear randomized rounding technique for linear programs, which could be useful in other application. Finally, we present improved hardness of approximation results for the weighted versions of the problem.