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31
Optimization of simple tabular reduction for table constraints
 In Proceedings of CP’08
, 2008
"... Abstract. Table constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints or/and to compress their representation. We show that simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamic ..."
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Cited by 25 (11 self)
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Abstract. Table constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints or/and to compress their representation. We show that simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports, is very often the most efficient practical approach to enforce generalized arc consistency within MAC. We also describe an optimization of STR which allows limiting the number of operations related to validity checking or search of supports. Interestingly enough, this optimization makes STR 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 the optimized algorithm we propose is usually around twice as fast as the original STR and can be up to one order of magnitude faster than previous stateoftheart algorithms on some series of instances. 1
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 ..."
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Cited by 10 (7 self)
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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 worstcase 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.
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 xbit CPU, one can then expect an increase of th ..."
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Cited by 9 (5 self)
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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 xbit 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 mwise consistency proposed in relational databases. We also define wR(∗,m)C, a weaker varia ..."
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Cited by 7 (5 self)
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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 mwise 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.
Abscon 109 A generic CSP solver
"... Abstract. This paper describes the algorithms, heuristics and general strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the second CSP solver competition. Both solvers maintain generalized arc consistency during search, explore the search space u ..."
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Cited by 5 (3 self)
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Abstract. This paper describes the algorithms, heuristics and general strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the second CSP solver competition. Both solvers maintain generalized arc consistency during search, explore the search space using a conflictdirected variable ordering heuristic, integrate nogood recording from restarts and exploit a transposition table approach to prune the search space. At preprocessing, the first solver enforces generalized arc consistency whereas the second one enforces existential SGAC, a partial form of singleton generalized arc consistency. 1
Efficient Algorithms for Singleton Arc Consistency
"... In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it require ..."
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Cited by 5 (4 self)
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In this paper, we propose two original and efficient approaches for enforcing singleton arc consistency. In the first one, the data structures used to enforce arc consistency are shared between all subproblems where a domain is reduced to a singleton. This new algorithm is not optimal but it requires far less space and is often more efficient in practice than the optimal algorithm SACOpt. In the second approach, we perform several runs of a greedy search (where at each step, arc consistency is maintained), possibly detecting the singleton arc consistency of several values in one run. It is an original illustration of applying inference (i.e., establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. We present extensive experiments that show the benefit of our two approaches.
Path Consistency by Dual Consistency
"... Abstract. Dual Consistency (DC) is a property of Constraint Networks (CNs) which is equivalent, in its unrestricted form, to Path Consistency (PC). The principle is to perform successive singleton checks (i.e. enforcing arc consistency after the assignment of a value to a variable) in order to ident ..."
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Cited by 5 (4 self)
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Abstract. Dual Consistency (DC) is a property of Constraint Networks (CNs) which is equivalent, in its unrestricted form, to Path Consistency (PC). The principle is to perform successive singleton checks (i.e. enforcing arc consistency after the assignment of a value to a variable) in order to identify inconsistent pairs of values, until a fixpoint is reached. In this paper, we propose two new algorithms, denoted by sDC2 and sDC3, to enforce (strong) PC following the DC approach. These algorithms can be seen as refinements of Mac Gregor’s algorithm as they partially and totally exploit the incrementality of the underlying Arc Consistency algorithm. While sDC3 admits the same interesting worstcase complexities as PC8, sDC2 appears to be the most robust algorithm in practice. Indeed, compared to PC8 and the optimal PC2001, sDC2 is usually around one order of magnitude faster on large instances. 1
Maintaining Arc Consistency with Multiple Residues
, 2013
"... Exploiting residual supports (or residues) has proved to be one of the most costeffective approaches for Maintaining Arc Consistency during search (MAC). While MAC based on optimal AC algorithm may have better theoretical time complexity in some cases, in practice the overhead for maintaining requi ..."
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Cited by 4 (1 self)
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Exploiting residual supports (or residues) has proved to be one of the most costeffective approaches for Maintaining Arc Consistency during search (MAC). While MAC based on optimal AC algorithm may have better theoretical time complexity in some cases, in practice the overhead for maintaining required data structure during search outweighs the benefit, not to mention the more complicated implementation. Implementing MAC with residues, on the other hand, is trivial. In this paper we extend previous work on residues and investigate the use of multiple residues during search. We first give a theoretical analysis of residuebased algorithms that explains their good practical performance. We then propose several heuristics on how to deal with multiple residues. Finally, our empirical study shows that with a proper and limited number of residues, many constraint checks can be saved. When the constraint check is expensive or a problem is hard, the multiple residues approach is competitive in both the number of constraint checks and cpu time.
Arc Consistency during Search
 In Proceedings of IJCAI2007
, 2007
"... Abstract Enforcing arc consistency (AC) during search has proven to be a very effective method in solving Constraint Satisfaction Problems and it has been widelyused in many Constraint Programming systems. Although much effort has been made to design efficient standalone AC algorithms, there is no ..."
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Cited by 4 (0 self)
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Abstract Enforcing arc consistency (AC) during search has proven to be a very effective method in solving Constraint Satisfaction Problems and it has been widelyused in many Constraint Programming systems. Although much effort has been made to design efficient standalone AC algorithms, there is no systematic study on how to efficiently enforce AC during search, as far as we know. The significance of the latter is clear given the fact that AC will be enforced millions of times in solving hard problems. In this paper, we propose a framework for enforcing AC during search (ACS) and complexity measurements of ACS algorithms. Based on this framework, several ACS algorithms are designed to take advantage of the residual data left in the data structures by the previous invocation(s) of ACS. The algorithms vary in the worstcase time and space complexity and other complexity measurements. Empirical study shows that some of the new ACS algorithms perform better than the conventional implementation of AC algorithms in a search procedure.
Generating Specialpurpose Stateless Propagators for Arbitrary Constraints
"... Abstract. Given an arbitrary constraint c on n variables with domain size d, we show how to generate a custom propagator that establishes GAC in time O(nd) by precomputing the propagation that would be performed on every reachable subdomain of scope(c). Our propagators are stateless: they store no s ..."
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Cited by 3 (1 self)
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Abstract. Given an arbitrary constraint c on n variables with domain size d, we show how to generate a custom propagator that establishes GAC in time O(nd) by precomputing the propagation that would be performed on every reachable subdomain of scope(c). Our propagators are stateless: they store no state between calls, and so incur no overhead in storing and backtracking state during search. The preprocessing step can take exponential time and the custom propagator is potentially exponential in size. However, for small constraints used repeatedly, in one problem or many, this technique can provide substantial practical gains. Our experimental results show that, compared with optimised implementations of the table constraint, this technique can lead to an order of magnitude speedup, while doing identical search on realistic problems. The technique can also be many times faster than a decomposition into primitive constraints in the Minion solver. Propagation is so fast that, for constraints available in our solver, the generated propagator compares well with a humanoptimised propagator for the same constraint. 1