124,457 research outputs found
Geographic Gossip: Efficient Averaging for Sensor Networks
Gossip algorithms for distributed computation are attractive due to their
simplicity, distributed nature, and robustness in noisy and uncertain
environments. However, using standard gossip algorithms can lead to a
significant waste in energy by repeatedly recirculating redundant information.
For realistic sensor network model topologies like grids and random geometric
graphs, the inefficiency of gossip schemes is related to the slow mixing times
of random walks on the communication graph. We propose and analyze an
alternative gossiping scheme that exploits geographic information. By utilizing
geographic routing combined with a simple resampling method, we demonstrate
substantial gains over previously proposed gossip protocols. For regular graphs
such as the ring or grid, our algorithm improves standard gossip by factors of
and respectively. For the more challenging case of random
geometric graphs, our algorithm computes the true average to accuracy
using radio
transmissions, which yields a factor improvement over
standard gossip algorithms. We illustrate these theoretical results with
experimental comparisons between our algorithm and standard methods as applied
to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin
Community structure in industrial SAT instances
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them.
In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version
Learning Laplacian Matrix in Smooth Graph Signal Representations
The construction of a meaningful graph plays a crucial role in the success of
many graph-based representations and algorithms for handling structured data,
especially in the emerging field of graph signal processing. However, a
meaningful graph is not always readily available from the data, nor easy to
define depending on the application domain. In particular, it is often
desirable in graph signal processing applications that a graph is chosen such
that the data admit certain regularity or smoothness on the graph. In this
paper, we address the problem of learning graph Laplacians, which is equivalent
to learning graph topologies, such that the input data form graph signals with
smooth variations on the resulting topology. To this end, we adopt a factor
analysis model for the graph signals and impose a Gaussian probabilistic prior
on the latent variables that control these signals. We show that the Gaussian
prior leads to an efficient representation that favors the smoothness property
of the graph signals. We then propose an algorithm for learning graphs that
enforces such property and is based on minimizing the variations of the signals
on the learned graph. Experiments on both synthetic and real world data
demonstrate that the proposed graph learning framework can efficiently infer
meaningful graph topologies from signal observations under the smoothness
prior
The edge-disjoint path problem on random graphs by message-passing
We present a message-passing algorithm to solve the edge disjoint path
problem (EDP) on graphs incorporating under a unique framework both traffic
optimization and path length minimization. The min-sum equations for this
problem present an exponential computational cost in the number of paths. To
overcome this obstacle we propose an efficient implementation by mapping the
equations onto a weighted combinatorial matching problem over an auxiliary
graph. We perform extensive numerical simulations on random graphs of various
types to test the performance both in terms of path length minimization and
maximization of the number of accommodated paths. In addition, we test the
performance on benchmark instances on various graphs by comparison with
state-of-the-art algorithms and results found in the literature. Our
message-passing algorithm always outperforms the others in terms of the number
of accommodated paths when considering non trivial instances (otherwise it
gives the same trivial results). Remarkably, the largest improvement in
performance with respect to the other methods employed is found in the case of
benchmarks with meshes, where the validity hypothesis behind message-passing is
expected to worsen. In these cases, even though the exact message-passing
equations do not converge, by introducing a reinforcement parameter to force
convergence towards a sub optimal solution, we were able to always outperform
the other algorithms with a peak of 27% performance improvement in terms of
accommodated paths. On random graphs, we numerically observe two separated
regimes: one in which all paths can be accommodated and one in which this is
not possible. We also investigate the behaviour of both the number of paths to
be accommodated and their minimum total length.Comment: 14 pages, 8 figure
Entangled networks, synchronization, and optimal network topology
A new family of graphs, {\it entangled networks}, with optimal properties in
many respects, is introduced. By definition, their topology is such that
optimizes synchronizability for many dynamical processes. These networks are
shown to have an extremely homogeneous structure: degree, node-distance,
betweenness, and loop distributions are all very narrow. Also, they are
characterized by a very interwoven (entangled) structure with short average
distances, large loops, and no well-defined community-structure. This family of
nets exhibits an excellent performance with respect to other flow properties
such as robustness against errors and attacks, minimal first-passage time of
random walks, efficient communication, etc. These remarkable features convert
entangled networks in a useful concept, optimal or almost-optimal in many
senses, and with plenty of potential applications computer science or
neuroscience.Comment: Slightly modified version, as accepted in Phys. Rev. Let
Network Codes for Real-Time Applications
We consider the scenario of broadcasting for real-time applications and loss
recovery via instantly decodable network coding. Past work focused on
minimizing the completion delay, which is not the right objective for real-time
applications that have strict deadlines. In this work, we are interested in
finding a code that is instantly decodable by the maximum number of users.
First, we prove that this problem is NP-Hard in the general case. Then we
consider the practical probabilistic scenario, where users have i.i.d. loss
probability and the number of packets is linear or polynomial in the number of
users. In this scenario, we provide a polynomial-time (in the number of users)
algorithm that finds the optimal coded packet. The proposed algorithm is
evaluated using both simulation and real network traces of a real-time Android
application. Both results show that the proposed coding scheme significantly
outperforms the state-of-the-art baselines: an optimal repetition code and a
COPE-like greedy scheme.Comment: ToN 2013 Submission Versio
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