Abstract
We present a simple algorithm for the maximum spanning star forest problem. We take advantage of the fact that the problem is a special case of complementary set cover and we adapt an algorithm of Duh and Fürer in order to solve it. We prove that this algorithm computes 193/240 ≈ 0.804-approximate spanning star forests; this result improves a previous lower bound of 0.71 by Chen et al. Although the algorithm is purely combinatorial, our analysis defines a linear program that uses a parameter f and which is feasible for values of the parameter f not smaller than the approximation ratio of the algorithm. The analysis is tight and, interestingly, it also applies to complementary versions of set cover such as color saving; it yields the same approximation guarantee of 193/240 that marginally improves the previously known upper bound of Duh and Fürer. We also show that, in general, a natural class of local search algorithms do not provide better than 1/2-approximate spanning star forests.
This work is partially supported by the European Union under IST FET Integrated Project FP6-015964 AEOLUS, by the General Secretariat for Research and Technology of the Greek Ministry of Development under programme PENED, and by a “Caratheodory” basic research grant from the University of Patras.
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Athanassopoulos, S., Caragiannis, I., Kaklamanis, C., Kyropoulou, M. (2009). An Improved Approximation Bound for Spanning Star Forest and Color Saving. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_9
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