Abstract
We give a general framework to handle node-connectivity degree constrained problems. In particular, for the k -Outconnected Subgraph problem, for both directed and undirected graphs, our algorithm computes in polynomial time a solution J of cost O(logk) times the optimal, such that deg J (v) = O(2k) ·b(v) for all v ∈ V. Similar result are obtained for the Element-Connectivity and the k -Connected Subgraph problems. The latter is a significant improvement on the particular case of only degree-approximation and undirected graphs considered in [5]. In addition, for the edge-connectivity directed Degree-Constrained k -Outconnected Subgraph problem, we slightly improve the best known approximation ratio, by a simple proof.
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Nutov, Z. (2012). Degree-Constrained Node-Connectivity. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_49
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DOI: https://doi.org/10.1007/978-3-642-29344-3_49
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