11,187 research outputs found
Decimation flows in constraint satisfaction problems
We study hard constraint satisfaction problems with a decimation approach
based on message passing algorithms. Decimation induces a renormalization flow
in the space of problems, and we exploit the fact that this flow transforms
some of the constraints into linear constraints over GF(2). In particular, when
the flow hits the subspace of linear problems, one can stop decimation and use
Gaussian elimination. We introduce a new decimation algorithm which uses this
linear structure and shows a strongly improved performance with respect to the
usual decimation methods on some of the hardest locked occupation problems.Comment: 14 pages, 2 figure
Building a Truly Distributed Constraint Solver with JADE
Real life problems such as scheduling meeting between people at different
locations can be modelled as distributed Constraint Satisfaction Problems
(CSPs). Suitable and satisfactory solutions can then be found using constraint
satisfaction algorithms which can be exhaustive (backtracking) or otherwise
(local search). However, most research in this area tested their algorithms by
simulation on a single PC with a single program entry point. The main
contribution of our work is the design and implementation of a truly
distributed constraint solver based on a local search algorithm using Java
Agent DEvelopment framework (JADE) to enable communication between agents on
different machines. Particularly, we discuss design and implementation issues
related to truly distributed constraint solver which might not be critical when
simulated on a single machine. Evaluation results indicate that our truly
distributed constraint solver works well within the observed limitations when
tested with various distributed CSPs. Our application can also incorporate any
constraint solving algorithm with little modifications.Comment: 7 page
Message passing algorithms for non-linear nodes and data compression
The use of parity-check gates in information theory has proved to be very
efficient. In particular, error correcting codes based on parity checks over
low-density graphs show excellent performances. Another basic issue of
information theory, namely data compression, can be addressed in a similar way
by a kind of dual approach. The theoretical performance of such a Parity Source
Coder can attain the optimal limit predicted by the general rate-distortion
theory. However, in order to turn this approach into an efficient compression
code (with fast encoding/decoding algorithms) one must depart from parity
checks and use some general random gates. By taking advantage of analytical
approaches from the statistical physics of disordered systems and SP-like
message passing algorithms, we construct a compressor based on low-density
non-linear gates with a very good theoretical and practical performance.Comment: 13 pages, European Conference on Complex Systems, Paris (Nov 2005
Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
The cluster variation method (CVM) is a hierarchy of approximate variational
techniques for discrete (Ising--like) models in equilibrium statistical
mechanics, improving on the mean--field approximation and the Bethe--Peierls
approximation, which can be regarded as the lowest level of the CVM. In recent
years it has been applied both in statistical physics and to inference and
optimization problems formulated in terms of probabilistic graphical models.
The foundations of the CVM are briefly reviewed, and the relations with
similar techniques are discussed. The main properties of the method are
considered, with emphasis on its exactness for particular models and on its
asymptotic properties.
The problem of the minimization of the variational free energy, which arises
in the CVM, is also addressed, and recent results about both provably
convergent and message-passing algorithms are discussed.Comment: 36 pages, 17 figure
Quiet Planting in the Locked Constraint Satisfaction Problems
We study the planted ensemble of locked constraint satisfaction problems. We
describe the connection between the random and planted ensembles. The use of
the cavity method is combined with arguments from reconstruction on trees and
first and second moment considerations; in particular the connection with the
reconstruction on trees appears to be crucial. Our main result is the location
of the hard region in the planted ensemble. In a part of that hard region
instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio
Message passing for quantified Boolean formulas
We introduce two types of message passing algorithms for quantified Boolean
formulas (QBF). The first type is a message passing based heuristics that can
prove unsatisfiability of the QBF by assigning the universal variables in such
a way that the remaining formula is unsatisfiable. In the second type, we use
message passing to guide branching heuristics of a Davis-Putnam
Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on
random QBFs our branching heuristics gives robust exponential efficiency gain
with respect to the state-of-art solvers. We also manage to solve some
previously unsolved benchmarks from the QBFLIB library. Apart from this our
study sheds light on using message passing in small systems and as subroutines
in complete solvers.Comment: 14 pages, 7 figure
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