Abstract
The minimum cost tree cover problem is to compute a minimum cost tree T in a given connected graph G with costs on the edges, such that the vertices of T form a vertex cover for G. The problem is supposed to arise in applications of vertex cover and edge dominating set when connectivity is additionally required in solutions. Whereas a linear-time 2-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is 3. Moreover, the known 3-approximation algorithm for such case is far from practical in its efficiency.
In this paper we present a fast, purely combinatorial 2-approximation algorithm for the minimum cost tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST), and to determine which leaves to trim, it uses both of the primal-dual schema and the local ratio technique in an interlaced fashion.
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Fujito, T. (2006). How to Trim an MST: A 2-Approximation Algorithm for Minimum Cost Tree Cover. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_38
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DOI: https://doi.org/10.1007/11786986_38
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