9,398 research outputs found
Controlled Hopwise Averaging: Bandwidth/Energy-Efficient Asynchronous Distributed Averaging for Wireless Networks
This paper addresses the problem of averaging numbers across a wireless
network from an important, but largely neglected, viewpoint: bandwidth/energy
efficiency. We show that existing distributed averaging schemes have several
drawbacks and are inefficient, producing networked dynamical systems that
evolve with wasteful communications. Motivated by this, we develop Controlled
Hopwise Averaging (CHA), a distributed asynchronous algorithm that attempts to
"make the most" out of each iteration by fully exploiting the broadcast nature
of wireless medium and enabling control of when to initiate an iteration. We
show that CHA admits a common quadratic Lyapunov function for analysis, derive
bounds on its exponential convergence rate, and show that they outperform the
convergence rate of Pairwise Averaging for some common graphs. We also
introduce a new way to apply Lyapunov stability theory, using the Lyapunov
function to perform greedy, decentralized, feedback iteration control. Finally,
through extensive simulation on random geometric graphs, we show that CHA is
substantially more efficient than several existing schemes, requiring far fewer
transmissions to complete an averaging task.Comment: 33 pages, 4 figure
The asymptotical error of broadcast gossip averaging algorithms
In problems of estimation and control which involve a network, efficient
distributed computation of averages is a key issue. This paper presents
theoretical and simulation results about the accumulation of errors during the
computation of averages by means of iterative "broadcast gossip" algorithms.
Using martingale theory, we prove that the expectation of the accumulated error
can be bounded from above by a quantity which only depends on the mixing
parameter of the algorithm and on few properties of the network: its size, its
maximum degree and its spectral gap. Both analytical results and computer
simulations show that in several network topologies of applicative interest the
accumulated error goes to zero as the size of the network grows large.Comment: 10 pages, 3 figures. Based on a draft submitted to IFACWC201
Greedy Gossip with Eavesdropping
This paper presents greedy gossip with eavesdropping (GGE), a novel
randomized gossip algorithm for distributed computation of the average
consensus problem. In gossip algorithms, nodes in the network randomly
communicate with their neighbors and exchange information iteratively. The
algorithms are simple and decentralized, making them attractive for wireless
network applications. In general, gossip algorithms are robust to unreliable
wireless conditions and time varying network topologies. In this paper we
introduce GGE and demonstrate that greedy updates lead to rapid convergence. We
do not require nodes to have any location information. Instead, greedy updates
are made possible by exploiting the broadcast nature of wireless
communications. During the operation of GGE, when a node decides to gossip,
instead of choosing one of its neighbors at random, it makes a greedy
selection, choosing the node which has the value most different from its own.
In order to make this selection, nodes need to know their neighbors' values.
Therefore, we assume that all transmissions are wireless broadcasts and nodes
keep track of their neighbors' values by eavesdropping on their communications.
We show that the convergence of GGE is guaranteed for connected network
topologies. We also study the rates of convergence and illustrate, through
theoretical bounds and numerical simulations, that GGE consistently outperforms
randomized gossip and performs comparably to geographic gossip on
moderate-sized random geometric graph topologies.Comment: 25 pages, 7 figure
Hamiltonian cycles in faulty random geometric networks
In this paper we analyze the Hamiltonian properties of
faulty random networks.
This consideration is of interest when considering wireless
broadcast networks.
A random geometric network is a graph whose vertices
correspond to points
uniformly and independently distributed in the unit square,
and whose edges
connect any pair of vertices if their distance is below some
specified bound.
A faulty random geometric network is a random geometric
network whose vertices
or edges fail at random. Algorithms to find Hamiltonian
cycles in faulty random
geometric networks are presented.Postprint (published version
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