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：网络化离散动力系统常被用于模拟传染病的传播以及协调博弈中智能体的决策过程。此类动力系统的不动点表示系统最终收敛到的配置。在不良传染源（如谣言和虚假信息）的传播中，使系统收敛到受影响节点数量较少的不动点是一个理想目标。基于此类考虑，我们提出一个新颖的优化问题：寻找系统中受影响节点数量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够逼近该问题解到因子n^1-ε以内。为应对这一计算难解性，我们识别出若干可高效求解该问题的特殊情况。此外，我们引入一个整数线性规划方法，以处理中等规模网络上的问题。针对更大规模网络上的求解，我们提出一个通用启发式框架，并结合贪心选择方法。在真实世界网络上的大量实验结果表明，所提启发式方法具有有效性。