  We consider the leader selection problem in a network with consensus dynamics
where both leader and follower agents are subject to stochastic external
disturbances. The performance of the system is quantified by the total
steady-state variance of the node states, and the goal is to identify the set
of leaders that minimizes this variance. We first show that this performance
measure can be expressed as a submodular set function over the nodes in the
network. We then use this result to analyze the performance of two greedy,
polynomial-time algorithms for leader selection, showing that the leader sets
produced by the greedy algorithms are within provable bounds of optimal.
