3,444 research outputs found
Reconstruction of Directed Networks from Consensus Dynamics
This paper addresses the problem of identifying the topology of an unknown,
weighted, directed network running a consensus dynamics. We propose a
methodology to reconstruct the network topology from the dynamic response when
the system is stimulated by a wide-sense stationary noise of unknown power
spectral density. The method is based on a node-knockout, or grounding,
procedure wherein the grounded node broadcasts zero without being eliminated
from the network. In this direction, we measure the empirical cross-power
spectral densities of the outputs between every pair of nodes for both grounded
and ungrounded consensus to reconstruct the unknown topology of the network. We
also establish that in the special cases of undirected or purely unidirectional
networks, the reconstruction does not need grounding. Finally, we extend our
results to the case of a directed network assuming a general dynamics, and
prove that the developed method can detect edges and their direction.Comment: 6 page
FROST -- Fast row-stochastic optimization with uncoordinated step-sizes
In this paper, we discuss distributed optimization over directed graphs,
where doubly-stochastic weights cannot be constructed. Most of the existing
algorithms overcome this issue by applying push-sum consensus, which utilizes
column-stochastic weights. The formulation of column-stochastic weights
requires each agent to know (at least) its out-degree, which may be impractical
in e.g., broadcast-based communication protocols. In contrast, we describe
FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an
optimization algorithm applicable to directed graphs that does not require the
knowledge of out-degrees; the implementation of which is straightforward as
each agent locally assigns weights to the incoming information and locally
chooses a suitable step-size. We show that FROST converges linearly to the
optimal solution for smooth and strongly-convex functions given that the
largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie
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