82,739 research outputs found
The Fractal Dimension of SAT Formulas
Modern SAT solvers have experienced a remarkable progress on solving
industrial instances. Most of the techniques have been developed after an
intensive experimental testing process. Recently, there have been some attempts
to analyze the structure of these formulas in terms of complex networks, with
the long-term aim of explaining the success of these SAT solving techniques,
and possibly improving them.
We study the fractal dimension of SAT formulas, and show that most industrial
families of formulas are self-similar, with a small fractal dimension. We also
show that this dimension is not affected by the addition of learnt clauses. We
explore how the dimension of a formula, together with other graph properties
can be used to characterize SAT instances. Finally, we give empirical evidence
that these graph properties can be used in state-of-the-art portfolios.Comment: 20 pages, 11 Postscript figure
LLAMA: Leveraging Learning to Automatically Manage Algorithms
Algorithm portfolio and selection approaches have achieved remarkable
improvements over single solvers. However, the implementation of such systems
is often highly customised and specific to the problem domain. This makes it
difficult for researchers to explore different techniques for their specific
problems. We present LLAMA, a modular and extensible toolkit implemented as an
R package that facilitates the exploration of a range of different portfolio
techniques on any problem domain. It implements the algorithm selection
approaches most commonly used in the literature and leverages the extensive
library of machine learning algorithms and techniques in R. We describe the
current capabilities and limitations of the toolkit and illustrate its usage on
a set of example SAT problems
A Multi-Engine Approach to Answer Set Programming
Answer Set Programming (ASP) is a truly-declarative programming paradigm
proposed in the area of non-monotonic reasoning and logic programming, that has
been recently employed in many applications. The development of efficient ASP
systems is, thus, crucial. Having in mind the task of improving the solving
methods for ASP, there are two usual ways to reach this goal: extending
state-of-the-art techniques and ASP solvers, or designing a new ASP
solver from scratch. An alternative to these trends is to build on top of
state-of-the-art solvers, and to apply machine learning techniques for choosing
automatically the "best" available solver on a per-instance basis.
In this paper we pursue this latter direction. We first define a set of
cheap-to-compute syntactic features that characterize several aspects of ASP
programs. Then, we apply classification methods that, given the features of the
instances in a {\sl training} set and the solvers' performance on these
instances, inductively learn algorithm selection strategies to be applied to a
{\sl test} set. We report the results of a number of experiments considering
solvers and different training and test sets of instances taken from the ones
submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows
that, by applying machine learning techniques to ASP solving, it is possible to
obtain very robust performance: our approach can solve more instances compared
with any solver that entered the 3rd ASP Competition. (To appear in Theory and
Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure
ASlib: A Benchmark Library for Algorithm Selection
The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa
An Enhanced Features Extractor for a Portfolio of Constraint Solvers
Recent research has shown that a single arbitrarily efficient solver can be
significantly outperformed by a portfolio of possibly slower on-average
solvers. The solver selection is usually done by means of (un)supervised
learning techniques which exploit features extracted from the problem
specification. In this paper we present an useful and flexible framework that
is able to extract an extensive set of features from a Constraint
(Satisfaction/Optimization) Problem defined in possibly different modeling
languages: MiniZinc, FlatZinc or XCSP. We also report some empirical results
showing that the performances that can be obtained using these features are
effective and competitive with state of the art CSP portfolio techniques
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