  Unions of graph multiplier operators are an important class of linear
operators for processing signals defined on graphs. We present a novel method
to efficiently distribute the application of these operators. The proposed
method features approximations of the graph multipliers by shifted Chebyshev
polynomials, whose recurrence relations make them readily amenable to
distributed computation. We demonstrate how the proposed method can be applied
to distributed processing tasks such as smoothing, denoising, inverse
filtering, and semi-supervised classification, and show that the communication
requirements of the method scale gracefully with the size of the network.
