  We consider a variety of NP-Complete network connectivity problems. We
introduce a novel dual-based approach to approximating network design problems
with cut-based linear programming relaxations. This approach gives a
$3/2$-approximation to Minimum 2-Edge-Connected Spanning Subgraph that is
equivalent to a previously proposed algorithm. One well-studied branch of
network design models ad hoc networks where each node can either operate at
high or low power. If we allow unidirectional links, we can formalize this into
the problem Dual Power Assignment (DPA). Our dual-based approach gives a
$3/2$-approximation to DPA, improving the previous best approximation known of
$11/7\approx 1.57$.
  Another standard network design problem is Minimum Strongly Connected
Spanning Subgraph (MSCS). We propose a new problem generalizing MSCS and DPA
called Star Strong Connectivity (SSC). Then we show that our dual-based
approach achieves a 1.6-approximation ratio on SSC. As a consequence of our
dual-based approximations, we prove new upper bounds on the integrality gaps of
these problems.
