  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.
