357 research outputs found
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
A methodology for full-system power modeling in heterogeneous data centers
The need for energy-awareness in current data centers has encouraged the use of power modeling to estimate their power consumption. However, existing models present noticeable limitations, which make them application-dependent, platform-dependent, inaccurate, or computationally complex. In this paper, we propose a platform-and application-agnostic methodology for full-system power modeling in heterogeneous data centers that overcomes those limitations. It derives a single model per platform, which works with high accuracy for heterogeneous applications with different patterns of resource usage and energy consumption, by systematically selecting a minimum set of resource usage indicators and extracting complex relations among them that capture the impact on energy consumption of all the resources in the system. We demonstrate our methodology by generating power models for heterogeneous platforms with very different power consumption profiles. Our validation experiments with real Cloud applications show that such models provide high accuracy (around 5% of average estimation error).This work is supported by the Spanish Ministry of Economy and Competitiveness under contract TIN2015-65316-P, by the Gener-
alitat de Catalunya under contract 2014-SGR-1051, and by the European Commission under FP7-SMARTCITIES-2013 contract 608679 (RenewIT) and FP7-ICT-2013-10 contracts 610874 (AS- CETiC) and 610456 (EuroServer).Peer ReviewedPostprint (author's final draft
Statistical Mechanics of the Hyper Vertex Cover Problem
We introduce and study a new optimization problem called Hyper Vertex Cover.
This problem is a generalization of the standard vertex cover to hypergraphs:
one seeks a configuration of particles with minimal density such that every
hyperedge of the hypergraph contains at least one particle. It can also be used
in important practical tasks, such as the Group Testing procedures where one
wants to detect defective items in a large group by pool testing. Using a
Statistical Mechanics approach based on the cavity method, we study the phase
diagram of the HVC problem, in the case of random regualr hypergraphs.
Depending on the values of the variables and tests degrees different situations
can occur: The HVC problem can be either in a replica symmetric phase, or in a
one-step replica symmetry breaking one. In these two cases, we give explicit
results on the minimal density of particles, and the structure of the phase
space. These problems are thus in some sense simpler than the original vertex
cover problem, where the need for a full replica symmetry breaking has
prevented the derivation of exact results so far. Finally, we show that
decimation procedures based on the belief propagation and the survey
propagation algorithms provide very efficient strategies to solve large
individual instances of the hyper vertex cover problem.Comment: Submitted to PR
The cavity method for large deviations
A method is introduced for studying large deviations in the context of
statistical physics of disordered systems. The approach, based on an extension
of the cavity method to atypical realizations of the quenched disorder, allows
us to compute exponentially small probabilities (rate functions) over different
classes of random graphs. It is illustrated with two combinatorial optimization
problems, the vertex-cover and coloring problems, for which the presence of
replica symmetry breaking phases is taken into account. Applications include
the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure
A novel method to identify sub-seasonal clustering episodes of extreme precipitation events and their contributions to large accumulation periods
Temporal (serial) clustering of extreme precipitation events on sub-seasonal time scales is a type of compound event. It can cause large precipitation accumulations and lead to floods. We present a novel, count-based procedure to identify episodes of sub-seasonal clustering of extreme precipitation. We introduce two metrics to characterise the frequency of sub-seasonal clustering episodes and their relevance for large precipitation accumulations. The procedure does not require the investigated variable (here precipitation) to satisfy any specific statistical properties. Applying this procedure to daily precipitation from the ERA5 reanalysis data set, we identify regions where sub-seasonal clustering occurs frequently and contributes substantially to large precipitation accumulations. The regions are the east and northeast of the Asian continent (north of Yellow Sea, in the Chinese provinces of Hebei, Jilin and Liaoning; North and South Korea; Siberia and east of Mongolia), central Canada and south of California, Afghanistan, Pakistan, the southwest of the Iberian Peninsula, and the north of Argentina and south of Bolivia. Our method is robust with respect to the parameters used to define the extreme events (the percentile threshold and the run length) and the length of the sub-seasonal time window (here 2–4 weeks). This procedure could also be used to identify temporal clustering of other variables (e.g. heat waves) and can be applied on different time scales (sub-seasonal to decadal). The code is available at the listed GitHub repository
The Phase Diagram of 1-in-3 Satisfiability Problem
We study the typical case properties of the 1-in-3 satisfiability problem,
the boolean satisfaction problem where a clause is satisfied by exactly one
literal, in an enlarged random ensemble parametrized by average connectivity
and probability of negation of a variable in a clause. Random 1-in-3
Satisfiability and Exact 3-Cover are special cases of this ensemble. We
interpolate between these cases from a region where satisfiability can be
typically decided for all connectivities in polynomial time to a region where
deciding satisfiability is hard, in some interval of connectivities. We derive
several rigorous results in the first region, and develop the
one-step--replica-symmetry-breaking cavity analysis in the second one. We
discuss the prediction for the transition between the almost surely satisfiable
and the almost surely unsatisfiable phase, and other structural properties of
the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure
Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
We study the entropy landscape of solutions for the bicoloring problem in
random graphs, a representative difficult constraint satisfaction problem. Our
goal is to classify which type of clusters of solutions are addressed by
different algorithms. In the first part of the study we use the cavity method
to obtain the number of clusters with a given internal entropy and determine
the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT
transitions. In the second part of the paper we analyze different algorithms
and locate their behavior in the entropy landscape of the problem. For instance
we show that a smoothed version of a decimation strategy based on Belief
Propagation is able to find solutions belonging to sub-dominant clusters even
beyond the so called rigidity transition where the thermodynamically relevant
clusters become frozen. These non-equilibrium solutions belong to the most
probable unfrozen clusters.Comment: 38 pages, 10 figure
Random multi-index matching problems
The multi-index matching problem (MIMP) generalizes the well known matching
problem by going from pairs to d-uplets. We use the cavity method from
statistical physics to analyze its properties when the costs of the d-uplets
are random. At low temperatures we find for d>2 a frozen glassy phase with
vanishing entropy. We also investigate some properties of small samples by
enumerating the lowest cost matchings to compare with our theoretical
predictions.Comment: 22 pages, 16 figure
An algorithm for counting circuits: application to real-world and random graphs
We introduce an algorithm which estimates the number of circuits in a graph
as a function of their length. This approach provides analytical results for
the typical entropy of circuits in sparse random graphs. When applied to
real-world networks, it allows to estimate exponentially large numbers of
circuits in polynomial time. We illustrate the method by studying a graph of
the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio
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