12,886 research outputs found
Topology design for fast convergence of network consensus algorithms
The quantities of coefficient of ergodicity and algebraic
connectivity have been used to estimate the convergence
rates of discrete-time and continuous-time network consensus
algorithms respectively. Both of these two quantities are defined
with respect to network topologies without the symmetry assumption,
and they are applicable to the case when network topologies
change with time. We present results identifying deterministic
network topologies that optimize these quantities. We will also
propose heuristics that can accelerate convergence in random
networks by redirecting a small portion of the links assuming
that the network topology is controllable.
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Sensor Networks with Random Links: Topology Design for Distributed Consensus
In a sensor network, in practice, the communication among sensors is subject
to:(1) errors or failures at random times; (3) costs; and(2) constraints since
sensors and networks operate under scarce resources, such as power, data rate,
or communication. The signal-to-noise ratio (SNR) is usually a main factor in
determining the probability of error (or of communication failure) in a link.
These probabilities are then a proxy for the SNR under which the links operate.
The paper studies the problem of designing the topology, i.e., assigning the
probabilities of reliable communication among sensors (or of link failures) to
maximize the rate of convergence of average consensus, when the link
communication costs are taken into account, and there is an overall
communication budget constraint. To consider this problem, we address a number
of preliminary issues: (1) model the network as a random topology; (2)
establish necessary and sufficient conditions for mean square sense (mss) and
almost sure (a.s.) convergence of average consensus when network links fail;
and, in particular, (3) show that a necessary and sufficient condition for both
mss and a.s. convergence is for the algebraic connectivity of the mean graph
describing the network topology to be strictly positive. With these results, we
formulate topology design, subject to random link failures and to a
communication cost constraint, as a constrained convex optimization problem to
which we apply semidefinite programming techniques. We show by an extensive
numerical study that the optimal design improves significantly the convergence
speed of the consensus algorithm and can achieve the asymptotic performance of
a non-random network at a fraction of the communication cost.Comment: Submitted to IEEE Transaction
Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems
In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons
On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
In decentralized consensus optimization, a connected network of agents
collaboratively minimize the sum of their local objective functions over a
common decision variable, where their information exchange is restricted
between the neighbors. To this end, one can first obtain a problem
reformulation and then apply the alternating direction method of multipliers
(ADMM). The method applies iterative computation at the individual agents and
information exchange between the neighbors. This approach has been observed to
converge quickly and deemed powerful. This paper establishes its linear
convergence rate for decentralized consensus optimization problem with strongly
convex local objective functions. The theoretical convergence rate is
explicitly given in terms of the network topology, the properties of local
objective functions, and the algorithm parameter. This result is not only a
performance guarantee but also a guideline toward accelerating the ADMM
convergence.Comment: 11 figures, IEEE Transactions on Signal Processing, 201
Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks
The performance of computer networks relies on how bandwidth is shared among
different flows. Fair resource allocation is a challenging problem particularly
when the flows evolve over time. To address this issue, bandwidth sharing
techniques that quickly react to the traffic fluctuations are of interest,
especially in large scale settings with hundreds of nodes and thousands of
flows. In this context, we propose a distributed algorithm based on the
Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path
fair resource allocation problem in a distributed SDN control architecture. Our
ADMM-based algorithm continuously generates a sequence of resource allocation
solutions converging to the fair allocation while always remaining feasible, a
property that standard primal-dual decomposition methods often lack. Thanks to
the distribution of all computer intensive operations, we demonstrate that we
can handle large instances at scale
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