Approximation to the minimum rooted star cover problem

Authors:
Wenbo Zhao;Peng Zhang
Affiliations:
State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China;State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

In this paper, we study the following minimum rooted star cover problem: given a complete graph G = (V,E) with a length function l : E → Z+ that satisfies the triangle inequality, a designated root vertex r ∈ V, and a length bound D, the objective is to find a minimum cardinality set of rooted stars, that covers all vertices in V such that the length of each rooted star is at most D, where a rooted star is a subset of E having a common center s ∈ V and containing the edge (r, s). This problem is NP-complete and we present a constant ratio approximation algorithm for this problem.