阈值模型中免疫接种的参数化复杂性
Parameterized Complexity of Immunization in the Threshold Model
摘要：
我们考虑控制网络中有害项目的传播问题，例如疾病的传染扩散或假新闻的传播。我们假设扩散的线性阈值模型，其中每个节点都有一个阈值来衡量节点对传染的抵抗力。我们研究的问题的参数化的复杂性：给定一个网络，一组最初污染的节点，和两个整数$k$和$\ell$，是否有可能限制扩散到最多$k$其他节点的网络免疫最多$\ell$节点？我们考虑了与输入相关的几个参数，包括：边界$k$和$\ell$，最大节点度$Δ$，树宽和网络的邻域多样性。我们首先给$W[1]$或$W[2]$ -硬度的结果为每个考虑的参数。然后，我们给出了一些参数组合的固定参数算法。
英文摘要：
We consider the problem of controlling the spread of harmful items in networks, such as the contagion proliferation of diseases or the diffusion of fake news. We assume the linear threshold model of diffusion where each node has a threshold that measures the node resistance to the contagion. We study the parameterized complexity of the problem: Given a network, a set of initially contaminated nodes, and two integers $k$ and $\ell$, is it possible to limit the diffusion to at most $k$ other nodes of the network by immunizing at most $\ell$ nodes? We consider several parameters associated to the input, including: the bounds $k$ and $\ell$, the maximum node degree $Δ$, the treewidth, and the neighborhood diversity of the network. We first give $W[1]$ or $W[2]$-hardness results for each of the considered parameters. Then we give fixed-parameter algorithms for some parameter combinations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
