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.
@article{arxiv.2005.14620,
title = {Parameterized Complexity of Min-Power Asymmetric Connectivity},
author = {Matthias Bentert and Roman Haag and Christian Hofer and Tomohiro Koana and André Nichterlein},
journal= {arXiv preprint arXiv:2005.14620},
year = {2020}
}