Leader Selection for Strong Structural Controllability in Networks using Zero Forcing Sets.

This paper studies the problem of computing a minimum zero forcing set (ZFS) in graphs. The problem is important because it is directly related to the leader selection problem for the strong structural controllability of networks defined over graphs. Computing a ZFS of minimum size is a well-known NP-hard problem in general. We show that previously known greedy heuristic could give arbitrarily bad solutions for some graphs. We study the problem on trees and present an optimal algorithm to compute a minimum ZFS in linear time in trees. For general graphs, we present a game-theoretic solution by formalizing the minimum ZFS problem as a potential game. Finally, we numerically evaluate our results on random graphs.