  We introduce group-to-group anycast (g2g-anycast), a network design problem
of substantial practical importance and considerable generality. Given a
collection of groups and requirements for directed connectivity from source
groups to destination groups, the solution network must contain, for each
requirement, an omni-directional down-link broadcast, centered at any node of
the source group, called the ball; the ball must contain some node from the
destination group in the requirement and all such destination nodes in the ball
must aggregate into a tree directed towards the source, called the funnel-tree.
The solution network is a collection of balls along with the funnel-trees they
contain. g2g-anycast models DBS (Digital Broadcast Satellite), Cable TV systems
and drone swarms. It generalizes several well known network design problems
including minimum energy unicast, multicast, broadcast, Steiner-tree,
Steiner-forest and Group-Steiner tree. Our main achievement is an $O(\log^4 n)$
approximation, counterbalanced by an $\log^{(2-\epsilon)}n$ hardness of
approximation, for general weights. Given the applicability to wireless
communication, we present a scalable and easily implemented $O(\log n)$
approximation algorithm, Cover-and-Grow for fixed-dimensional Euclidean space
with path-loss exponent at least 2.
