STR2: Optimized Simple Tabular Reduction for Table Constraints

International audienceTable constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints and/or to compress their representation. In this paper, we describe an optimization of simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports when generalized arc consistency (GAC) is enforced/maintained. STR2, the new refined GAC algorithm we propose, allows us to limit the number of operations related to validity checking and search of supports. Interestingly enough, this optimization makes simple tabular reduction potentially r times faster where r is the arity of the constraint(s). The results of an extensive experimentation that we have conducted with respect to random and structured instances indicate that STR2 is usually around twice as fast as the original STR, two or three times faster than the approach based on the hidden variable encoding, and can be up to one order of magnitude faster than previously state-of-the art (generic) GAC algorithms on some series of instances. When comparing STR2 with the more recently developed algorithm based on multi-valued decision diagrams (MDDs), we show that both approaches are rather complementary

A Simple Model to Generate Hard Satisfiable Instances

In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features. First, it is quite easy to generate random instances of any arity since no particular structure has to be integrated, or property enforced, in such instances. Then, the existence of an asymptotic phase transition can be guaranteed while applying a limited restriction on domain size and on constraint tightness. In that case, a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold, i.e., to have an exponential tree-resolution complexity. Next, a formal analysis shows that it is possible to generate forced satisfiable instances whose hardness is similar to unforced satisfiable ones. This analysis is supported by some representative results taken from an intensive experimentation that we have carried out, using complete and incomplete search methods.Comment: Proc. of 19th IJCAI, pp.337-342, Edinburgh, Scotland, 2005. For more information, please click http://www.nlsde.buaa.edu.cn/~kexu/papers/ijcai05-abstract.ht

Abscon 112: towards more robustness

dans le cadre de CP'08International audienceThis paper describes the three main improvements made to the solver Abscon 109 [9]. The new version, Abscon 112, is able to automatically break some variable symmetries, infer allDifferent constraints from cliques of variables that are pair-wise irreexive, and use an optimized version of the STR (Simple Tabular Reduction) technique initially introduced by J. Ullmann for table constraints

Cohérences basées sur les valeurs en échec

International audienceNon disponibl

Une étude des supports résiduels pour la consistance d'arc

Pour un algorithme établissant la consistance d'arc (AC), un support résiduel, ou résidu, est un support qui a été trouvé et enregistré lors d'une exécution de la procédure qui détermine si une valeur est supportée par une contrainte. Le point important est qu'un résidu n'offre pas la garantie de représenter un minorant du plus petit support courant de la valeur en question. Dans cet article, nous étudions l'impact théorique d'exploiter des résidus au niveau de l'algorithme élémentaire AC3. Tout d'abord, nous prouvons que AC3r(m) (i.e. AC3 exploitant des résidus) est optimal pour une dureté de contrainte faible ou élevée. Ensuite, nous montrons que MAC2001 présente, par rapport à MAC3r(m), un sur-coût en O(μed) par branche de l'arbre binaire construit par MAC, avec μ représentant le nombre de réfutations de la branche, e le nombre de contraintes et d la taille du plus grand domaine. L'une des conséquences est que, MAC3r(m) admet une complexité temporelle (dans le pire des cas) meilleure que MAC2001 pour une branche impliquant μ réfutations lorsque μ > d2 ou lorsque μ > d et que la dureté de chaque contrainte est soit faible soit élevée. Nos résultats expérimentaux montrent clairement que le fait d'exploiter des résidus permet d'améliorer l'efficacité des algorithmes MAC et SAC embarquant des algorithmes AC à gros grain

Symmetry-reinforced Nogood Recording from Restarts

dans le cadre de CP'11International audienceNogood recording from restarts is a form of lightweight learn- ing that combines nogood recording with a restart strategy. At the end of each run, nogoods are extracted from the current (rightmost) branch of the search tree. These nogoods can be used to prevent parts of the search space from being explored more than once. In this paper, we propose to reinforce nogood recording (from restarts) by exploiting symmetries: every time the solver has to be restarted, not only the nogoods that are extracted from the current branch are recorded, but also some additional nogoods that can be computed by means of the previously identi ed problem symmetries. This mechanism of computing symmetric nogoods can be iterated until a xed-point is reached, and controlled (if necessary) by limiting the number and/or the size of recorded nogoods

PYCSP3: Modeling Combinatorial Constrained Problems in Python

In this document, we introduce PYCSP$3$, a Python library that allows us to write models of combinatorial constrained problems in a simple and declarative way. Currently, with PyCSP$3$, you can write models of constraint satisfaction and optimization problems. More specifically, you can build CSP (Constraint Satisfaction Problem) and COP (Constraint Optimization Problem) models. Importantly, there is a complete separation between modeling and solving phases: you write a model, you compile it (while providing some data) in order to generate an XCSP3 instance (file), and you solve that problem instance by means of a constraint solver. In this document, you will find all that you need to know about PYCSP$3$, with more than 40 illustrative models

Lightweight Detection of Variable Symmetries for Constraint Satisfaction

International audienceIn this paper, we propose to automatically detect vari- able symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetric variables. From this local information obtained in polyno- mial time, we can build a so-called lsv-graph whose auto- morphisms correspond to (global) variable symmetries. In- terestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constra ints. Besides, the size of the lsv-graph is linear with respect to the number of constraints (and their arity)

Une approche gloutonne pour établir la singleton consistance d'arc

http://www710.univ-lyon1.fr/~csolnonDans cet article, nous proposons une nouvelle approche pour établir la singleton consistance d'arc (SAC) d'un réseau de contraintes. Tandis que le principe des algorithmes SAC existants consiste à réaliser un parcours en largeur d'abord jusqu'à une profondeur égale à 1, le principe des deux algorithmes que nous introduisons consiste à réaliser plusieurs exécutions d'une recherche gloutonne (telle que la consistance d'arc soit maintenue à chaque étape). Il s'agit d'une illustration originale d'inférence (i.e. établir la singleton consistance d'arc) par la recherche. Utiliser une approche gloutonne permet de bénéficier de l'incrémentalité de la consistance d'arc, d'apprendre des informations pertinentes à partir des conflits et de, potentiellement, trouver des solutions pendant le processus d'inférence. De plus, les complexités temporelle et spatiale sont tout à fait compétitives

XML Representation of Constraint Networks: Format XCSP 2.1

We propose a new extended format to represent constraint networks using XML. This format allows us to represent constraints defined either in extension or in intension. It also allows us to reference global constraints. Any instance of the problems CSP (Constraint Satisfaction Problem), QCSP (Quantified CSP) and WCSP (Weighted CSP) can be represented using this format