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Degree Constrained Node-Connectivity Problems

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Abstract

We consider Degree Constrained Survivable Network problems. For the directed Degree Constrained k -Edge-Outconnected Subgraph problem, we slightly improve the best known approximation ratio, by a simple proof. Our main contribution is giving a framework to handle node-connectivity degree constrained problems with the iterative rounding method. In particular, for the degree constrained versions of the Element-Connectivity Survivable Network problem on undirected graphs, and of the k -Outconnected Subgraph problem on both directed and undirected graphs, our algorithm computes a solution J of cost O(logk) times the optimal, with degrees O(2k)⋅b(v). Similar result are obtained for the k -Connected Subgraph problem. The latter improves on the only degree approximation O(klogn)⋅b(v) in O(n k) time on undirected graphs by Feder, Motwani, and Zhu.

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Acknowledgements

I thank Jochen Könemann for drawing my attention that no non-trivial algorithm was known for Degree Constrained Element-Connectivity Survivable Network problem. I also thank Rohit Khandekar and Guy Kortsarz for some discussions.

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  1. The Open University of Israel, Raánana, Israel

    Zeev Nutov

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  1. Zeev Nutov
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Correspondence to Zeev Nutov.

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Nutov, Z. Degree Constrained Node-Connectivity Problems. Algorithmica 70, 340–364 (2014). https://doi.org/10.1007/s00453-013-9849-1

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