57,978 research outputs found
Sensitive Instances of the Constraint Satisfaction Problem
We investigate the impact of modifying the constraining relations of a
Constraint Satisfaction Problem (CSP) instance, with a fixed template, on the
set of solutions of the instance. More precisely we investigate sensitive
instances: an instance of the CSP is called sensitive, if removing any tuple
from any constraining relation invalidates some solution of the instance.
Equivalently, one could require that every tuple from any one of its
constraints extends to a solution of the instance.
Clearly, any non-trivial template has instances which are not sensitive.
Therefore we follow the direction proposed (in the context of strict width) by
Feder and Vardi (SICOMP 1999) and require that only the instances produced by a
local consistency checking algorithm are sensitive. In the language of the
algebraic approach to the CSP we show that a finite idempotent algebra
has a variable near unanimity term operation if and only if
any instance that results from running the -consistency algorithm on
an instance over is sensitive.
A version of our result, without idempotency but with the sensitivity
condition holding in a variety of algebras, settles a question posed by G.
Bergman about systems of projections of algebras that arise from some
subalgebra of a finite product of algebras.
Our results hold for infinite (albeit in the case of idempotent)
algebras as well and exhibit a surprising similarity to the strict width
condition proposed by Feder and Vardi. Both conditions can be characterized by
the existence of a near unanimity operation, but the arities of the operations
differ by 1
Sensitive instances of the constraint satisfaction problem
We investigate the impact of modifying the constraining relations of a Constraint SatisfactionProblem (CSP) instance, with a fixed template, on the set of solutions of the instance. More preciselywe investigate sensitive instances: an instance of theCSPis called sensitive, if removing any tuplefrom any constraining relation invalidates some solution of the instance. Equivalently, one couldrequire that every tuple from any one of its constraints extends to a solution of the instance.Clearly, any non-trivial template has instances which are not sensitive. Therefore we follow thedirection proposed (in the context of strict width) by Feder and Vardi in [13] and require that onlythe instances produced by a local consistency checking algorithm are sensitive. In the languageof the algebraic approach to theCSPwe show that a finite idempotent algebraAhas ak+ 2variable near unanimity term operation if and only if any instance that results from running the(k, k+ 1)-consistency algorithm on an instance overA2is sensitive.A version of our result, without idempotency but with the sensitivity condition holding in avariety of algebras, settles a question posed by G. Bergman about systems of projections of algebrasthat arise from some subalgebra of a finite product of algebras.Our results hold for infinite (albeit in the case ofAidempotent) algebras as well and exhibit asurprising similarity to the strict widthkcondition proposed by Feder and Vardi. Both conditionscan be characterized by the existence of a near unanimity operation, but the arities of the operationsdiffer by1
Metareasoning about propagators for constraint satisfaction
Given the breadth of constraint satisfaction problems (CSPs) and the wide variety of CSP solvers, it is often very difficult to determine a priori which solving method is best suited to a problem. This work explores the use of machine learning to predict which solving method will be most effective for a given problem. We use four different problem sets to determine the CSP attributes that can be used to determine which solving method should be applied. After choosing an appropriate set of attributes, we determine how well j48 decision trees can predict which solving method to apply. Furthermore, we take a cost sensitive approach such that problem instances where there is a great difference in runtime between algorithms are emphasized. We also attempt to use information gained on one class of problems to inform decisions about a second class of problems. Finally, we show that the additional costs of deciding which method to apply are outweighed by the time savings compared to applying the same solving method to all problem instances
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
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
Rational Deployment of CSP Heuristics
Heuristics are crucial tools in decreasing search effort in varied fields of
AI. In order to be effective, a heuristic must be efficient to compute, as well
as provide useful information to the search algorithm. However, some well-known
heuristics which do well in reducing backtracking are so heavy that the gain of
deploying them in a search algorithm might be outweighed by their overhead.
We propose a rational metareasoning approach to decide when to deploy
heuristics, using CSP backtracking search as a case study. In particular, a
value of information approach is taken to adaptive deployment of solution-count
estimation heuristics for value ordering. Empirical results show that indeed
the proposed mechanism successfully balances the tradeoff between decreasing
backtracking and heuristic computational overhead, resulting in a significant
overall search time reduction.Comment: 7 pages, 2 figures, to appear in IJCAI-2011, http://www.ijcai.org
Proteus: A Hierarchical Portfolio of Solvers and Transformations
In recent years, portfolio approaches to solving SAT problems and CSPs have
become increasingly common. There are also a number of different encodings for
representing CSPs as SAT instances. In this paper, we leverage advances in both
SAT and CSP solving to present a novel hierarchical portfolio-based approach to
CSP solving, which we call Proteus, that does not rely purely on CSP solvers.
Instead, it may decide that it is best to encode a CSP problem instance into
SAT, selecting an appropriate encoding and a corresponding SAT solver. Our
experimental evaluation used an instance of Proteus that involved four CSP
solvers, three SAT encodings, and six SAT solvers, evaluated on the most
challenging problem instances from the CSP solver competitions, involving
global and intensional constraints. We show that significant performance
improvements can be achieved by Proteus obtained by exploiting alternative
view-points and solvers for combinatorial problem-solving.Comment: 11th International Conference on Integration of AI and OR Techniques
in Constraint Programming for Combinatorial Optimization Problems. The final
publication is available at link.springer.co
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Experimental evaluation of preprocessing algorithms for constraint satisfaction problems
This paper presents an experimental evaluation of two orthogonal schemes for preprocessing constraint satisfaction problems (CSPs). The first of these schemes involves a class of local consistency techniques that includes directional arc consistency, directional path consistency, and adaptive consistency. The other scheme concerns the prearrangement of variables in a linear order to facilitate an efficient search. In the first series of experiments, we evaluated the effect of each of the local consistency techniques on backtracking and its common enhancement, backjumping. Surprizingly, although adaptive consistency has the best worst-case complexity bounds, we have found that it exhibits the worst performance, unless the constraint graph was very sparse. Directional arc consistency (followed by either backjumping or backtracking) and backjumping (without any pre-processing) outperformed all other techniques; moreover, the former dominated the latter in computationally intensive situations. The second series of experiments suggests that maximum cardinality and minimum width arc the best pre-ordering (i.e., static ordering) strategies, while dynamic search rearrangement is superior to all the preorderings studied
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