Degree constrained node-connectivity problems

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(2 ^k )·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.