10,684 research outputs found
Organic Design of Massively Distributed Systems: A Complex Networks Perspective
The vision of Organic Computing addresses challenges that arise in the design
of future information systems that are comprised of numerous, heterogeneous,
resource-constrained and error-prone components or devices. Here, the notion
organic particularly highlights the idea that, in order to be manageable, such
systems should exhibit self-organization, self-adaptation and self-healing
characteristics similar to those of biological systems. In recent years, the
principles underlying many of the interesting characteristics of natural
systems have been investigated from the perspective of complex systems science,
particularly using the conceptual framework of statistical physics and
statistical mechanics. In this article, we review some of the interesting
relations between statistical physics and networked systems and discuss
applications in the engineering of organic networked computing systems with
predictable, quantifiable and controllable self-* properties.Comment: 17 pages, 14 figures, preprint of submission to Informatik-Spektrum
published by Springe
Distributed Convergence Verification for Gaussian Belief Propagation
Gaussian belief propagation (BP) is a computationally efficient method to
approximate the marginal distribution and has been widely used for inference
with high dimensional data as well as distributed estimation in large-scale
networks. However, the convergence of Gaussian BP is still an open issue.
Though sufficient convergence conditions have been studied in the literature,
verifying these conditions requires gathering all the information over the
whole network, which defeats the main advantage of distributed computing by
using Gaussian BP. In this paper, we propose a novel sufficient convergence
condition for Gaussian BP that applies to both the pairwise linear Gaussian
model and to Gaussian Markov random fields. We show analytically that this
sufficient convergence condition can be easily verified in a distributed way
that satisfies the network topology constraint.Comment: accepted by Asilomar Conference on Signals, Systems, and Computers,
2017, Asilomar, Pacific Grove, CA. arXiv admin note: text overlap with
arXiv:1706.0407
Generating constrained random graphs using multiple edge switches
The generation of random graphs using edge swaps provides a reliable method
to draw uniformly random samples of sets of graphs respecting some simple
constraints, e.g. degree distributions. However, in general, it is not
necessarily possible to access all graphs obeying some given con- straints
through a classical switching procedure calling on pairs of edges. We therefore
propose to get round this issue by generalizing this classical approach through
the use of higher-order edge switches. This method, which we denote by "k-edge
switching", makes it possible to progres- sively improve the covered portion of
a set of constrained graphs, thereby providing an increasing, asymptotically
certain confidence on the statistical representativeness of the obtained
sample.Comment: 15 page
Convergence analysis of the information matrix in Gaussian belief propagation
Gaussian belief propagation (BP) has been widely used for distributed
estimation in large-scale networks such as the smart grid, communication
networks, and social networks, where local measurements/observations are
scattered over a wide geographical area. However, the convergence of Gaus- sian
BP is still an open issue. In this paper, we consider the convergence of
Gaussian BP, focusing in particular on the convergence of the information
matrix. We show analytically that the exchanged message information matrix
converges for arbitrary positive semidefinite initial value, and its dis- tance
to the unique positive definite limit matrix decreases exponentially fast.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0201
Polynomial Linear Programming with Gaussian Belief Propagation
Interior-point methods are state-of-the-art algorithms for solving linear
programming (LP) problems with polynomial complexity. Specifically, the
Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where
is the number of unknown variables. Karmarkar's celebrated algorithm is known
to be an instance of the log-barrier method using the Newton iteration. The
main computational overhead of this method is in inverting the Hessian matrix
of the Newton iteration. In this contribution, we propose the application of
the Gaussian belief propagation (GaBP) algorithm as part of an efficient and
distributed LP solver that exploits the sparse and symmetric structure of the
Hessian matrix and avoids the need for direct matrix inversion. This approach
shifts the computation from realm of linear algebra to that of probabilistic
inference on graphical models, thus applying GaBP as an efficient inference
engine. Our construction is general and can be used for any interior-point
algorithm which uses the Newton method, including non-linear program solvers.Comment: 7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on
Communication, Control and Computing, Allerton House, Illinois, Sept. 200
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