Abstract: A core requirement in distributed
systems and networks is to disseminate information from certain nodes
to other nodes. In this talk, we discuss a linear iterative strategy
for information dissemination, where each node repeatedly updates its
value to be a weighted linear combination of its previous value and
those of its neighbors. We show that this strategy can be compactly
modeled as a linear dynamical system, and that common information
dissemination tasks can be viewed in the context of certain properties
of linear systems. Specifically, we make the following connections: (1)
accumulating all of the data in the network at certain nodes can be
viewed as an observability problem, (2) accumulating all of the data
despite the presence of malicious nodes in the network can be viewed as
a strong observability problem, and (3) transmitting streams of data
from source nodes to sink nodes can be viewed as an invertibility
problem.
These connections allow us to
leverage tools from structured system theory to design linear iterative
strategies to disseminate information in networks. Finally, we discuss
the extension of these results to systems over finite fields, and show
how this can be applied to the problems of estimation and control in
multi-agent systems with quantization constraints.