High Dimensional Robust Consensus Over Networks With Limited Capacity

We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number state variables that can be communicated instantaneously. When capacities are small compared to dimensionality vectors, it not possible instantaneously communicate full information every edge. how (small steady variance states) achieved within a time-invariant setting by optimally assigning edges state-dimensions. show finite states if and only minimum cut network smaller than vectors. Optimal approximate solutions provided for some special classes graphs. also consider related problem allocating additional feasible initial solution. this corresponds maximization submodular function subject matroid constraint, which approximated via greedy algorithm.