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. [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.
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Chen, N., Engelberg, R., Nguyen, C.T., Raghavendra, P., Rudra, A., Singh, G. (2007). Improved Approximation Algorithms for the Spanning Star Forest Problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_4
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DOI: https://doi.org/10.1007/978-3-540-74208-1_4
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