Locally constructed algorithms for distributed computations in ad-hoc networks

In this paper we develop algorithms for distributed computation of a broad range of estimation and detection tasks over networks with arbitrary but fixed connectivity. The distributed algorithms we develop are linear dynamical systems that generate sequences of approximations to the desired computation. The algorithms are locally constructed at each node by exploiting only locally available and macroscopic information about the network topology. We present methods for designing these distributed algorithms so as to optimize the convergence rates to the desired computation and demonstrate their performance characteristics in the context of a problem of signal estimation from multi-node signal observations in Gaussian noise.