49 research outputs found
The Configurable SAT Solver Challenge (CSSC)
It is well known that different solution strategies work well for different
types of instances of hard combinatorial problems. As a consequence, most
solvers for the propositional satisfiability problem (SAT) expose parameters
that allow them to be customized to a particular family of instances. In the
international SAT competition series, these parameters are ignored: solvers are
run using a single default parameter setting (supplied by the authors) for all
benchmark instances in a given track. While this competition format rewards
solvers with robust default settings, it does not reflect the situation faced
by a practitioner who only cares about performance on one particular
application and can invest some time into tuning solver parameters for this
application. The new Configurable SAT Solver Competition (CSSC) compares
solvers in this latter setting, scoring each solver by the performance it
achieved after a fully automated configuration step. This article describes the
CSSC in more detail, and reports the results obtained in its two instantiations
so far, CSSC 2013 and 2014
Warmstarting of Model-based Algorithm Configuration
The performance of many hard combinatorial problem solvers depends strongly
on their parameter settings, and since manual parameter tuning is both tedious
and suboptimal the AI community has recently developed several algorithm
configuration (AC) methods to automatically address this problem. While all
existing AC methods start the configuration process of an algorithm A from
scratch for each new type of benchmark instances, here we propose to exploit
information about A's performance on previous benchmarks in order to warmstart
its configuration on new types of benchmarks. We introduce two complementary
ways in which we can exploit this information to warmstart AC methods based on
a predictive model. Experiments for optimizing a very flexible modern SAT
solver on twelve different instance sets show that our methods often yield
substantial speedups over existing AC methods (up to 165-fold) and can also
find substantially better configurations given the same compute budget.Comment: Preprint of AAAI'18 pape
Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is
applied to the optimization of a large hard instance of the Random 3-SAT
Problem (N=10000). The dynamical behavior of the quantum and the classical
annealing are compared, showing important qualitative differences in the way of
exploring the complex energy landscape of the combinatorial optimization
problem. At variance with the results obtained for the Ising spin glass and for
the Traveling Salesman Problem, in the present case the linear-schedule Quantum
Annealing performance is definitely worse than Classical Annealing.
Nevertheless, a quantum cooling protocol based on field-cycling and able to
outperform standard classical simulated annealing over short time scales is
introduced.Comment: 10 pages, 6 figures, submitted to PR
Moments of Autocorrelation Demerit Factors of Binary Sequences
Sequences with low aperiodic autocorrelation are used in communications and
remote sensing for synchronization and ranging. The autocorrelation demerit
factor of a sequence is the sum of the squared magnitudes of its
autocorrelation values at every nonzero shift when we normalize the sequence to
have unit Euclidean length. The merit factor, introduced by Golay, is the
reciprocal of the demerit factor. We consider the uniform probability measure
on the binary sequences of length and investigate the
distribution of the demerit factors of these sequences. Previous researchers
have calculated the mean and variance of this distribution. We develop new
combinatorial techniques to calculate the th central moment of the demerit
factor for binary sequences of length . These techniques prove that for
and , all the central moments are strictly positive. For
any given , one may use the technique to obtain an exact formula for the
th central moment of the demerit factor as a function of the length .
The previously obtained formula for variance is confirmed by our technique with
a short calculation, and we demonstrate that our techniques go beyond this by
also deriving an exact formula for the skewness.Comment: 40 page
Multireference Alignment using Semidefinite Programming
The multireference alignment problem consists of estimating a signal from
multiple noisy shifted observations. Inspired by existing Unique-Games
approximation algorithms, we provide a semidefinite program (SDP) based
relaxation which approximates the maximum likelihood estimator (MLE) for the
multireference alignment problem. Although we show that the MLE problem is
Unique-Games hard to approximate within any constant, we observe that our
poly-time approximation algorithm for the MLE appears to perform quite well in
typical instances, outperforming existing methods. In an attempt to explain
this behavior we provide stability guarantees for our SDP under a random noise
model on the observations. This case is more challenging to analyze than
traditional semi-random instances of Unique-Games: the noise model is on
vertices of a graph and translates into dependent noise on the edges.
Interestingly, we show that if certain positivity constraints in the SDP are
dropped, its solution becomes equivalent to performing phase correlation, a
popular method used for pairwise alignment in imaging applications. Finally, we
show how symmetry reduction techniques from matrix representation theory can
simplify the analysis and computation of the SDP, greatly decreasing its
computational cost