  We investigate parameterized algorithms for the NP-hard problem Min-Power
Asymmetric Connectivity (MinPAC) that has applications in wireless sensor
networks. Given a directed arc-weighted graph, MinPAC asks for a strongly
connected spanning subgraph minimizing the summed vertex costs. Here, the cost
of each vertex is the weight of its heaviest outgoing arc in the chosen
subgraph. We present linear-time algorithms for the cases where the number of
strongly connected components in a so-called obligatory subgraph or the
feedback edge number in the underlying undirected graph is constant.
Complementing these results, we prove that the problem is W[2]-hard with
respect to the solution cost, even on restricted graphs with one feedback arc
and binary arc weights.
