We investigate multivariate algorithms for the NP-hard Min-Power Asymmetric Connectivity (MinPAC) problem that has applications in wireless sensor networks. Given a directed arc-weighted n-vertex 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. 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.
CITATION STYLE
Bentert, M., Haag, R., Hofer, C., Koana, T., & Nichterlein, A. (2019). Parameterized complexity of Min-Power asymmetric connectivity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11638 LNCS, pp. 85–96). Springer Verlag. https://doi.org/10.1007/978-3-030-25005-8_8
Mendeley helps you to discover research relevant for your work.