High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed algorithm, when the number of samples n=omega(J_{min}^{-2} log p), where p is the number of variables and J_{min} is the minimum (absolute) edge potential of the graphical model. The sufficient conditions for sparsistency are based on the notion of walk-summability of the model and the presence of sparse local vertex separators in the underlying graph. We also derive novel non-asymptotic necessary conditions on the number of samples required for sparsistency

Multi-hop Byzantine reliable broadcast with honest dealer made practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g., digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment