Finite-time distributed consensus through graph filters

We propose a new framework for distributed computation of average consensus. The presented framework leads to a systematic design of iterative algorithms that compute the consensus exactly, are guaranteed to converge in finite time, are computationally efficient, and require no online memory. We demonstrate that our approach is applicable to a broad class of networks. For remaining networks, our framework leads to the construction of approximating algorithms for consensus that are also guaranteed to compute in finite time. Our approach is inspired by graph filters introduced by the theoretical framework of signal processing on graphs.