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In a standard $f$-connectivity network design problem, we are given anundirected graph $G=(V,E)$, a cut-requirement function $f:2^V \rightarrow{\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \in E$. We are thenasked to find a minimum-cost vector $x \in {\mathbb{N}}^E$ such that$x(\delta(S)) \geq f(S)$ for all $S \subseteq V$. We focus on the class of suchproblems where $f$ is a proper function. This encodes many well-studied NP-hardproblems such as the generalized survivable network design problem.  In this paper we present the first strongly polynomial time FPTAS for solvingthe LP relaxation of the standard IP formulation of the $f$-connectivityproblem with general proper functions $f$. Implementing Jain's algorithm, thisyields a strongly polynomial time $(2+\epsilon)$-approximation for thegeneralized survivable network design problem (where we consider rounding up ofrationals an arithmetic operation).

Fast Approximation Algorithms for the Generalized Survivable Network Design Problem