2 research outputs found
Multiscale Gossip for Efficient Decentralized Averaging in Wireless Packet Networks
This paper describes and analyzes a hierarchical gossip algorithm for solving
the distributed average consensus problem in wireless sensor networks. The
network is recursively partitioned into subnetworks. Initially, nodes at the
finest scale gossip to compute local averages. Then, using geographic routing
to enable gossip between nodes that are not directly connected, these local
averages are progressively fused up the hierarchy until the global average is
computed. We show that the proposed hierarchical scheme with levels of
hierarchy is competitive with state-of-the-art randomized gossip algorithms, in
terms of message complexity, achieving -accuracy with high
probability after
messages. Key to our analysis is the way in which the network is recursively
partitioned. We find that the optimal scaling law is achieved when subnetworks
at scale contain nodes; then the message complexity at any
individual scale is , and the total number of
scales in the hierarchy grows slowly, as . Another
important consequence of hierarchical construction is that the longest distance
over which messages are exchanged is hops (at the highest scale),
and most messages (at lower scales) travel shorter distances. In networks that
use link-level acknowledgements, this results in less congestion and resource
usage by reducing message retransmissions. Simulations illustrate that the
proposed scheme is more message-efficient than existing state-of-the-art
randomized gossip algorithms based on averaging along paths.Comment: (under Review
A Double-Layered Framework for Distributed Coordination in Solving Linear Equations
This paper proposes a double-layered framework (or form of network) to
integrate two mechanisms, termed consensus and conservation, achieving
distributed solution of a linear equation. The multi-agent framework considered
in the paper is composed of clusters (which serve as a form of aggregating
agent) and each cluster consists of a sub-network of agents. By achieving
consensus and conservation through agent-agent communications in the same
cluster and cluster-cluster communications, distributed algorithms are devised
for agents to cooperatively achieve a solution to the overall linear equation.
These algorithms outperform existing consensus-based algorithms, including but
not limited to the following aspects: first, each agent does not have to know
as much as a complete row or column of the overall equation; second, each agent
only needs to control as few as two scalar states when the number of clusters
and the number of agents are sufficiently large; third, the dimensions of
agents' states in the proposed algorithms do not have to be the same (while in
contrast, algorithms based on the idea of standard consensus inherently require
all agents' states to be of the same dimension). Both analytical proof and
simulation results are provided to validate exponential convergence of the
proposed distributed algorithms in solving linear equations