Results 11 - 20
of
92
An MDD-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints, Constraints 15 (2
, 2010
"... Abstract. A table constraint is explicitly represented its set of solu-tions or non-solutions. This ad hoc (or extensional) representation may require space exponential to the arity of the constraint, making enforcing GAC expensive. In this paper, we address the space and time inefficien-cies simult ..."
Abstract
-
Cited by 18 (1 self)
- Add to MetaCart
(Show Context)
Abstract. A table constraint is explicitly represented its set of solu-tions or non-solutions. This ad hoc (or extensional) representation may require space exponential to the arity of the constraint, making enforcing GAC expensive. In this paper, we address the space and time inefficien-cies simultaneously by presenting the mddc constraint. mddc is a global constraint that represents its (non-)solutions with a multi-valued deci-sion diagram (MDD). The MDD-based representation has the advantage that it can be exponentially smaller than a table. The associated GAC algorithm (called mddc) has time complexity linear to the size of the MDD, and achieves full incrementality in constant time. In addition, we show how to convert a positive or negative table constraint into an mddc constraint in time linear to the size of the table. Our experiments on structured problems, car sequencing and still-life, show that mddc is also a fast GAC algorithm for some global constraints such as sequence and regular. We also show that mddc is faster than the state-of-the-art generic GAC algorithms in [2–4] for table constraint. 1
Consistency and the Quantified Constraint Satisfaction Problem
, 2007
"... Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving unc ..."
Abstract
-
Cited by 16 (1 self)
- Add to MetaCart
Constraint satisfaction is a very well studied and fundamental artificial intelligence technique. Various forms of knowledge can be represented with constraints, and reasoning techniques from disparate fields can be encapsulated within constraint reasoning algorithms. However, problems involving uncertainty, or which have an adversarial nature (for example, games), are difficult to express and solve in the classical constraint satisfaction problem. This thesis is concerned with an extension to the classical problem: the Quantified Constraint Satisfaction Problem (QCSP). QCSP has recently attracted interest. In QCSP, quantifiers are allowed, facilitating the expression of uncertainty. I examine whether QCSP is a useful formalism. This divides into two questions: whether QCSP can be solved efficiently; and whether realistic problems can be represented in QCSP. In attempting to answer these questions, the main contributions of this thesis are the following: • the definition of two new notions of consistency; • four new constraint propagation algorithms (with eight variants in total), along with em-pirical evaluations;
Nogood recording from restarts
- In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI’2007
, 2007
"... In this paper, nogood recording is investigated within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next one. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search algorithm. ..."
Abstract
-
Cited by 15 (3 self)
- Add to MetaCart
(Show Context)
In this paper, nogood recording is investigated within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next one. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search algorithm. Such a set of nogoods is extracted from the last branch of the current search tree. Interestingly, the number of nogoods recorded before each new run is bounded by the length of the last branch of the search tree. As a consequence, the total number of recorded nogoods is polynomial in the number of restarts. Experiments over a wide range of CSP instances demonstrate the effectiveness of our approach. 1
Advisors for Incremental Propagation
- THIRTEENTH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2007
"... While incremental propagation for global constraints is recognized to be important, little research has been devoted to how propagator-centered constraint programming systems should support incremental propagation. This paper introduces advisors as a simple and efficient, yet widely applicable metho ..."
Abstract
-
Cited by 14 (2 self)
- Add to MetaCart
While incremental propagation for global constraints is recognized to be important, little research has been devoted to how propagator-centered constraint programming systems should support incremental propagation. This paper introduces advisors as a simple and efficient, yet widely applicable method for supporting incremental propagation in a propagator-centered setting. The paper presents how advisors can be used for achieving different forms of incrementality and evaluates cost and benefit for several global constraints.
Reformulation of global constraints based on constraints checkers
- CONSTRAINTS 10(4):339–362
, 2005
"... This article deals with global constraints for which the set of solutions can be recognized by an extended nite automaton whose size is bounded by a polynomial in n, where n is the number of variables of the corresponding global constraint. By reducing the automaton to a conjunction of signature a ..."
Abstract
-
Cited by 10 (3 self)
- Add to MetaCart
(Show Context)
This article deals with global constraints for which the set of solutions can be recognized by an extended nite automaton whose size is bounded by a polynomial in n, where n is the number of variables of the corresponding global constraint. By reducing the automaton to a conjunction of signature and transition constraints we show how to systematically obtain an automaton re-formulation. Under some restrictions on the signature and transition constraints, this reformulation maintains arc-consistency. An implementation based on some constraints as well as on the metaprogramming facilities of SICStus Prolog is available. For a restricted class of automata we provide an automaton reformu-lation for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution.
Conservative Dual Consistency
- In Proceedings of AAAI’07
, 2007
"... Consistencies are properties of Constraint Networks (CNs) that can be exploited in order to make inferences. When a significant amount of such inferences can be performed, CNs are much easier to solve. In this paper, we interest ourselves in relation filtering consistencies for binary constraints, i ..."
Abstract
-
Cited by 10 (7 self)
- Add to MetaCart
(Show Context)
Consistencies are properties of Constraint Networks (CNs) that can be exploited in order to make inferences. When a significant amount of such inferences can be performed, CNs are much easier to solve. In this paper, we interest ourselves in relation filtering consistencies for binary constraints, i.e. consistencies that allow to identify inconsistent pairs of values. We propose a new consistency called Dual Consistency (DC) and relate it to Path Consistency (PC). We show that Conservative DC (CDC, i.e. DC with only relations associated with the constraints of the network considered) is more powerful, in terms of filtering, than Conservative PC (CPC). Following the approach of Mac Gregor, we introduce an algorithm to establish (strong) CDC with a very low worst-case space complexity. Even if the relative efficiency of the algorithm introduced to establish (strong) CDC partly depends on the density of the constraint graph, the experiments we have conducted show that, on many series of CSP instances, CDC is largely faster than CPC (up to more than one order of magnitude). Besides, we have observed that enforcing CDC in a preprocessing stage can significantly speed up the resolution of hard structured instances.
Last conflict based reasoning
- In Proceedings of ECAI-2006
, 2006
"... Abstract. In this paper, we propose an approach to guide search to sources of conflicts. The principle is the following: the last variable involved in the last conflict is selected in priority, as long as the constraint network can not be made consistent, in order to find the (most recent) culprit v ..."
Abstract
-
Cited by 9 (1 self)
- Add to MetaCart
(Show Context)
Abstract. In this paper, we propose an approach to guide search to sources of conflicts. The principle is the following: the last variable involved in the last conflict is selected in priority, as long as the constraint network can not be made consistent, in order to find the (most recent) culprit variable, following the current partial instantiation from the leaf to the root of the search tree. In other words, the variable ordering heuristic is violated, until a backtrack to the culprit variable occurs and a singleton consistent value is found. Consequently, this way of reasoning can easily be grafted to many search algorithms and represents an original way to avoid thrashing. Experiments over a wide range of benchmarks demonstrate the effectiveness of this approach. 1
Enforcing Arc Consistency using Bitwise Operations
- CONSTRAINT PROGRAMMING LETTERS
, 2007
"... In this paper, we propose to exploit bitwise operations to speed up some important computations such as looking for a support of a value in a constraint, or determining if a value is substitutable by another one. Considering a computer equipped with a x-bit CPU, one can then expect an increase of th ..."
Abstract
-
Cited by 9 (5 self)
- Add to MetaCart
In this paper, we propose to exploit bitwise operations to speed up some important computations such as looking for a support of a value in a constraint, or determining if a value is substitutable by another one. Considering a computer equipped with a x-bit CPU, one can then expect an increase of the performance by a coefficient up to x (which may be important, since x is equal to 32 or 64 in many current central units). To show the interest of enforcing arc consistency using bitwise operations, we introduce a new variant of AC3, denoted by AC3 bit, which can be used when constraints are (or can be) represented in extension. This new algorithm when embedded in MAC, is approximately two times more efficient than AC3 rm. Note that AC3 rm is a variant of AC3 which exploits the concept of residual supports and has been shown to be faster than AC2001.
A First Practical Algorithm for High Levels of Relational Consistency
- IN: 24 TH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 2010
"... Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(∗,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(∗,m)C, a weaker varia ..."
Abstract
-
Cited by 7 (5 self)
- Add to MetaCart
(Show Context)
Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(∗,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(∗,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(∗,m)C solves in a backtrackfree manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.
An Analysis of Slow Convergence in Interval Propagation
"... Abstract. When performing interval propagation on integer variables with a large range, slow-convergence phenomena are often observed: it becomes difficult to reach the fixpoint of the propagation. This problem is practically important, as it hinders the use of propagation techniques for problems wi ..."
Abstract
-
Cited by 7 (1 self)
- Add to MetaCart
(Show Context)
Abstract. When performing interval propagation on integer variables with a large range, slow-convergence phenomena are often observed: it becomes difficult to reach the fixpoint of the propagation. This problem is practically important, as it hinders the use of propagation techniques for problems with large numerical ranges, and notably problems arising in program verification. A number of attempts to cope with this issue have been investigated, yet all of the proposed techniques only guarantee a fast convergence on specific instances. An important question is therefore whether slow convergence is intrinsic to propagation methods, or whether an improved propagation algorithm may exist that would avoid this problem. This paper proposes the first analysis of the slow convergence problem under the light of complexity results. It answers the question, by a negative result: if we allow propagators that are general enough, computing the fixpoint of constraint propagation is shown to be intractable. Slow convergence is therefore unavoidable unless P=NP. The result holds for the propagators of a basic class of constraints. 1
