  In the classical survivable network design problem (SNDP), we are given an
undirected graph $G=(V,E)$ with costs on edges and a connectivity requirement
$k(s,t)$ for each pair of vertices. The goal is to find a minimum-cost subgraph
$H\subseteq V$ such that every pair $(s,t)$ are connected by $k(s,t)$ edge or
(openly) vertex disjoint paths, abbreviated as EC-SNDP and VC-SNDP,
respectively. The seminal result of Jain [FOCS'98, Combinatorica'01] gives a
$2$-approximation algorithm for EC-SNDP, and a decade later, an $O(k^3\log
n)$-approximation algorithm for VC-SNDP, where $k$ is the largest connectivity
requirement, was discovered by Chuzhoy and Khanna [FOCS'09, Theory Comput.'12].
While there is rich literature on point-to-point settings of SNDP, the viable
case of connectivity between subsets is still relatively poorly understood.
  This paper concerns the generalization of SNDP into the subset-to-subset
setting, namely Group EC-SNDP. We develop the framework, which yields the first
non-trivial (true) approximation algorithm for Group EC-SNDP. Previously, only
a bicriteria approximation algorithm is known for Group EC-SNDP [Chalermsook,
Grandoni, and Laekhanukit, SODA'15], and a true approximation algorithm is
known only for the single-source variant with connectivity requirement
$k(S,T)\in\{0,1,2\}$ [Gupta, Krishnaswamy, and Ravi, SODA'10; Khandekar,
Kortsarz, and Nutov, FSTTCS'09 and Theor. Comput. Sci.'12].
