Abstract
We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, Minimum Edge Dominating Set and Minimum Maximal Matching. We show that it is NP-hard to approximate the solution of both problems to within any constant factor smaller than \(\frac{7}{6}\). The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs.
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Chlebík, M., Chlebíková, J. (2003). Approximation Hardness of Minimum Edge Dominating Set and Minimum Maximal Matching. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_43
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DOI: https://doi.org/10.1007/978-3-540-24587-2_43
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