235 research outputs found
Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning under structural
restrictions. All these problems involve two tasks: (i) identifying the
structure in the input as required by the restriction, and (ii) using the
identified structure to solve the reasoning task efficiently. We show that for
most of the considered problems, task (i) admits a polynomial-time
preprocessing to a problem kernel whose size is polynomial in a structural
problem parameter of the input, in contrast to task (ii) which does not admit
such a reduction to a problem kernel of polynomial size, subject to a
complexity theoretic assumption. As a notable exception we show that the
consistency problem for the AtMost-NValue constraint admits a polynomial kernel
consisting of a quadratic number of variables and domain values. Our results
provide a firm worst-case guarantees and theoretical boundaries for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541,
arXiv:1104.556
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
Generalizing backdoors
Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.
La contrainte Increasing NValue
National audienceCet article introduit la contrainte Increasing NValue, qui restreint le nombre de valeurs distinctes affectées à une séquence de variables, de sorte que chaque variable de la séquence soit inférieure ou égale à la variable la succédant immédiatement. Cette contrainte est une spécialisation de la contrainte NValue, motivée par le besoin de casser des symétries. Il est bien connu que propager la contrainte NValue est un problème NP-Difficile. Nous montrons que la spécialisation au cas d'une séquence ordonnée de variables rend le problème polynomial. Nous proposons un algorithme d'arc-consistance ayant une complexité temporelle en O(sum D), où sum D est la somme des tailles des domaines. Cet algorithme est une amélioration significative, en termes de complexité, des algorithmes issus d'une représentation de la contrainte Increasing NValue à l'aide d'automates ou de la contrainte SLIDE. Nous utilisons notre contrainte dans le cadre d'un problème d'allocation de ressources
On the Reification of Global Constraints
We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on
the observation that most global constraints can be reformulated as a conjunction of pure functional dependency
constraints together with a constraint that can be easily reified. We first show how the core constraints of the
Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at
least 82% of the constraints in the Global Constraint Catalogue
A Generalized Arc-Consistency Algorithm for a Class of Counting Constraints: Revised Edition that Incorporates One Correction
This paper introduces the SEQ BIN meta-constraint with a polytime algorithm
achieving general- ized arc-consistency according to some properties. SEQ BIN
can be used for encoding counting con- straints such as CHANGE, SMOOTH or
INCREAS- ING NVALUE. For some of these constraints and some of their variants
GAC can be enforced with a time and space complexity linear in the sum of
domain sizes, which improves or equals the best known results of the
literature
Global Constraint Catalog, 2nd Edition (revision a)
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
Global Constraint Catalog, 2nd Edition
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
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