153 research outputs found
Decentralized Constraint Satisfaction
We show that several important resource allocation problems in wireless
networks fit within the common framework of Constraint Satisfaction Problems
(CSPs). Inspired by the requirements of these applications, where variables are
located at distinct network devices that may not be able to communicate but may
interfere, we define natural criteria that a CSP solver must possess in order
to be practical. We term these algorithms decentralized CSP solvers. The best
known CSP solvers were designed for centralized problems and do not meet these
criteria. We introduce a stochastic decentralized CSP solver and prove that it
will find a solution in almost surely finite time, should one exist, also
showing it has many practically desirable properties. We benchmark the
algorithm's performance on a well-studied class of CSPs, random k-SAT,
illustrating that the time the algorithm takes to find a satisfying assignment
is competitive with stochastic centralized solvers on problems with order a
thousand variables despite its decentralized nature. We demonstrate the
solver's practical utility for the problems that motivated its introduction by
using it to find a non-interfering channel allocation for a network formed from
data from downtown Manhattan
Large-scale parallelism for constraint-based local search: the costas array case study
International audienceWe present the parallel implementation of a constraint-based Local Search algorithm and investigate its performance on several hardware plat-forms with several hundreds or thousands of cores. We chose as the basis for these experiments the Adaptive Search method, an efficient sequential Local Search method for Constraint Satisfaction Problems (CSP). After preliminary experiments on some CSPLib benchmarks, we detail the modeling and solving of a hard combinatorial problem related to radar and sonar applications: the Costas Array Problem. Performance evaluation on some classical CSP bench-marks shows that speedups are very good for a few tens of cores, and good up to a few hundreds of cores. However for a hard combinatorial search problem such as the Costas Array Problem, performance evaluation of the sequential version shows results outperforming previous Local Search implementations, while the parallel version shows nearly linear speedups up to 8,192 cores. The proposed parallel scheme is simple and based on independent multi-walks with no communication between processes during search. We also investigated a cooperative multi-walk scheme where processes share simple information, but this scheme does not seem to improve performance
Biased landscapes for random Constraint Satisfaction Problems
The typical complexity of Constraint Satisfaction Problems (CSPs) can be
investigated by means of random ensembles of instances. The latter exhibit many
threshold phenomena besides their satisfiability phase transition, in
particular a clustering or dynamic phase transition (related to the tree
reconstruction problem) at which their typical solutions shatter into
disconnected components. In this paper we study the evolution of this
phenomenon under a bias that breaks the uniformity among solutions of one CSP
instance, concentrating on the bicoloring of k-uniform random hypergraphs. We
show that for small k the clustering transition can be delayed in this way to
higher density of constraints, and that this strategy has a positive impact on
the performances of Simulated Annealing algorithms. We characterize the modest
gain that can be expected in the large k limit from the simple implementation
of the biasing idea studied here. This paper contains also a contribution of a
more methodological nature, made of a review and extension of the methods to
determine numerically the discontinuous dynamic transition threshold.Comment: 32 pages, 16 figure
Stochastic Control via Entropy Compression
We consider an agent trying to bring a system to an acceptable state by
repeated probabilistic action. Several recent works on algorithmizations of the
Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for
the agent to succeed. Here we study whether such stochastic control is also
possible in a noisy environment, where both the process of state-observation
and the process of state-evolution are subject to adversarial perturbation
(noise). The introduction of noise causes the tools developed for LLL
algorithmization to break down since the key LLL ingredient, the sparsity of
the causality (dependence) relationship, no longer holds. To overcome this
challenge we develop a new analysis where entropy plays a central role, both to
measure the rate at which progress towards an acceptable state is made and the
rate at which noise undoes this progress. The end result is a sufficient
condition that allows a smooth tradeoff between the intensity of the noise and
the amenability of the system, recovering an asymmetric LLL condition in the
noiseless case.Comment: 18 page
Perturbative large deviation analysis of non-equilibrium dynamics
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium
stochastic dynamical systems obey a large deviation principle, but except for a
few one-dimensional examples these large deviation principles are in general
not known in closed form. We consider the problem of constructing successive
approximations to an (unknown) large deviation functional and show that the
non-equilibrium probability distribution the takes a Gibbs-Boltzmann form with
a set of auxiliary (non-physical) energy functions. The expectation values of
these auxiliary energy functions and their conjugate quantities satisfy a
closed system of equations which can imply a considerable reduction of
dimensionality of the dynamics. We show that the accuracy of the approximations
can be tested self-consistently without solving the full non- equilibrium
equations. We test the general procedure on the simple model problem of a
relaxing 1D Ising chain.Comment: 21 pages, 10 figure
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