Improved Approximation Algorithms for the Spanning Star Forest Problem

Authors:
Ning Chen;Roee Engelberg;C. Thach Nguyen;Prasad Raghavendra;Atri Rudra;Gyanit Singh
Affiliations:
Department of Computer Science & Engineering, University of Washington, Seattle, USA;Department of Computer Science, Technion, Haifa, Israel;Department of Computer Science & Engineering, University of Washington, Seattle, USA;Department of Computer Science & Engineering, University of Washington, Seattle, USA;Department of Computer Science & Engineering, University of Washington, Seattle, USA;Department of Computer Science & Engineering, University of Washington, Seattle, USA
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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Abstract

A stargraph is a tree of diameter at most two. A star forestis 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 Gand has the maximum number of edges. This problem is the complement of the dominating set problem in the following sense: On a graph with nvertices, the size of the maximum spanning star forest is equal to nminus 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.