Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the dissemination of undesirable contagions (such as rumors and misinformation), convergence to fixed points with a small number of affected nodes is a desirable goal. Motivated by such considerations, we formulate a novel optimization problem of finding a nontrivial fixed point of the system with the minimum number of affected nodes. We establish that, unless P = NP, there is no polynomial time algorithm for approximating a solution to this problem to within the factor n^1-\epsilon for any constant epsilon > 0. To cope with this computational intractability, we identify several special cases for which the problem can be solved efficiently. Further, we introduce an integer linear program to address the problem for networks of reasonable sizes. For solving the problem on larger networks, we propose a general heuristic framework along with greedy selection methods. Extensive experimental results on real-world networks demonstrate the effectiveness of the proposed heuristics.

翻译：网络化离散动态系统常用于模拟传染病传播及协调博弈中智能体的决策过程。此类动态系统的不动点代表系统收敛到的配置状态。在不良传染病（如谣言和错误信息）传播场景中，收敛到受感染节点数量较少的固定点是理想目标。基于此考量，我们提出一个新颖的优化问题：寻找系统中受感染节点数最少的非平凡不动点。我们证明，除非P=NP，否则对于任意常数ε>0，不存在多项式时间算法能将该问题的解逼近至n^1-ε因子范围内。为应对这种计算复杂性，我们识别出若干可高效求解该问题的特殊情形。进一步，我们引入整数线性规划方法处理中等规模网络的该问题。针对更大规模网络的求解，我们提出基于贪心选择策略的通用启发式框架。在真实网络上的大量实验结果表明，所提启发式算法具有显著有效性。