  This paper investigates the computational complexity of sparse label
propagation which has been proposed recently for processing network structured
data. Sparse label propagation amounts to a convex optimization problem and
might be considered as an extension of basis pursuit from sparse vectors to
network structured datasets. Using a standard first-order oracle model, we
characterize the number of iterations for sparse label propagation to achieve a
prescribed accuracy. In particular, we derive an upper bound on the number of
iterations required to achieve a certain accuracy and show that this upper
bound is sharp for datasets having a chain structure (e.g., time series).
