Abstract
A forest cover of a graph is a spanning forest for which each component has at least two nodes. IfK is a subset of nodes, aK-forest cover is a forest cover including exactly one node fromK in each component. AK-forest cover is of minimum cost if the sum of the costs of the edges is minimum. We present an0(n 2 + ¦K¦2 n) algorithm for determining the minimum costK-forest cover of a graph withn nodes. We show that the algorithm can also be used to determine, in0(n 2 + ({K — K'¦ + ∑ deK'd v )2 n ) time, the minimum costK-forest cover having degree equald v each nodev of an arbitrary subsetK' ofK.
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Baas, S.M., Cerdeira, J.O. Minimum costK-forest covers. Mathematical Methods of Operations Research 44, 255–265 (1996). https://doi.org/10.1007/BF01194334
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DOI: https://doi.org/10.1007/BF01194334