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.

我们研究了针对NP难题最小功率不对称连接（MinPAC）的参数化算法，该算法已在无线传感器网络中得到应用。给定一个有向弧加权图，MinPAC要求一个强连接的跨子图，以最大程度地降低总顶点成本。在这里，每个顶点的成本是所选子图中最重的向外弧的权重。对于所谓的强制子图中强连接的组件数或基础无向图中的反馈边数是恒定的情况，我们提出了线性时间算法。补充这些结果，我们证明即使在具有一个反馈弧和二元弧权重的受限图上，就解决方案成本而言，该问题也是W [2]难题。