Manufacturing Consent

We consider a variant of the gossip algorithm wherein a controller can influence the values at a subset of nodes as well as the averaging weights. This leads to three optimization problems: (i) Optimal choice of nodes: a combinatorial optimization problem for which we propose a nonlinear programming relaxation as well as a greedy heuristic; (ii) Parametric optimization of weights: a non-convex optimization for which we propose an effective heuristic for a special case; (iii) Dynamic adjustment of weights: an optimal control problem. For the dynamic case, we note some empirically observed interesting critical phenomena for the uncontrolled case.