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18
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
An MDDbased 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 solutions or nonsolutions. 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 inefficiencies simult ..."
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Cited by 18 (1 self)
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Abstract. A table constraint is explicitly represented its set of solutions or nonsolutions. 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 inefficiencies simultaneously by presenting the mddc constraint. mddc is a global constraint that represents its (non)solutions with a multivalued decision diagram (MDD). The MDDbased 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 stilllife, 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 stateoftheart generic GAC algorithms in [2–4] for table constraint. 1
Abscon 112 Toward more Robustness
"... Abstract. This 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 pairwise irreflexive, and use an optimized version of ..."
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Cited by 6 (0 self)
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Abstract. This 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 pairwise irreflexive, and use an optimized version of the STR (Simple Tabular Reduction) technique initially introduced by J. Ullmann for table constraints. 1 From Local to Global Variable Symmetries In [10], we have proposed to automatically detect variable symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetrical variables. From this local information that can be obtained in polynomial time, we can build a socalled lsvgraph whose automorphisms correspond to (global) variable symmetries. Interestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constraints. Besides, the size of the lsvgraph is linear wrt the number of constraints (and their arity). To break symmetries from the generators returned by a graph automorphism
A PathOptimal GAC Algorithm for Table Constraints
 20TH EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (ECAI'12), FRANCE
, 2012
"... Filtering by Generalized Arc Consistency (GAC) is a fundamental technique in Constraint Programming. Recent advances in GAC algorithms for extensional constraints rely on direct manipulation of tables during search. Simple Tabular Reduction (STR), which systematically removes invalid tuples from ta ..."
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Cited by 6 (2 self)
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Filtering by Generalized Arc Consistency (GAC) is a fundamental technique in Constraint Programming. Recent advances in GAC algorithms for extensional constraints rely on direct manipulation of tables during search. Simple Tabular Reduction (STR), which systematically removes invalid tuples from tables, has been shown to be a simple yet efficient approach. STR2, a refinement of STR, is considered to be among the best filtering algorithms for positive table constraints. In this paper, we introduce a new GAC algorithm called STR3 that is specifically designed to enforce GAC during search. STR3 can completely avoid unnecessary traversal of tables, making it optimal along any path of the search tree. Our experiments show that STR3 is much faster than STR2 when the average size of the tables is not reduced drastically during search.
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.
Encoding Table Constraints in CLP(FD) Based on Pairwise AC
"... Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime r ..."
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Cited by 3 (3 self)
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Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime removal of unsupported values. For nary constraints, we propose pairwise arc consistency (AC), which ensures that each value has a support in the domain of every related variable. Pairwise AC does not require introducing new problem variables as done in binarization methods and allows for compact representation of constraints. Nevertheless, pairwise AC is weaker than general arc consistency (GAC) in terms of pruning power and requires a final check when a constraint becomes ground. To remedy this weakness, we propose adopting early checks when constraints are sufficiently instantiated. Our experimentation shows that pairwise AC with early checking is as effective as GAC for positive constraints. 1
An Optimal Filtering Algorithm for Table Constraints
"... Filtering algorithms for table constraints are constraintbased, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient valuebased algorithms for table constraints, meaning that the propagation queue also co ..."
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Cited by 3 (1 self)
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Filtering algorithms for table constraints are constraintbased, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient valuebased algorithms for table constraints, meaning that the propagation queue also contains information on the removed values. One of these algorithms (AC5TCTr) is proved to have an optimal time complexity of O(r.t + r.d) per table constraint. Experimental results show that, on structured instances, all our algorithms are two or three times faster than the state of the art STR2+ and MDD c algorithms.
Propagating Soft Table Constraints
 18TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP'12), QUÉBEC: CANADA
, 2012
"... WCSP is a framework that has attracted a lot of attention during the last decade. In particular, many filtering approaches have been developed on the concept of equivalencepreserving transformations (cost transfer operations), using the definition of soft local consistencies such as, for example, ..."
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Cited by 2 (2 self)
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WCSP is a framework that has attracted a lot of attention during the last decade. In particular, many filtering approaches have been developed on the concept of equivalencepreserving transformations (cost transfer operations), using the definition of soft local consistencies such as, for example, node consistency, arc consistency, full directional arc consistency, and existential directional arc consistency. Almost all algorithms related to these properties have been introduced for binary weighted constraint networks, and most of the conducted experiments typically include networks with binary and ternary constraints only. In this paper, we focus on extensional soft constraints (of large arity), socalled soft table constraints. We propose an algorithm to enforce a soft version of generalized arc consistency (GAC) on such constraints, by combining both the techniques of cost transfer and simple tabular reduction, the latter dynamically maintaining the list of allowed tuples in constraint tables. On various series of problem instances containing soft table constraints of large arity, we show the practical interest of our approach.
Extending Simple Tabular Reduction with Short Supports
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2013
"... Constraint propagation is one of the key techniques in constraint programming, and a large body of work has built up around it. Specialpurpose constraint propagation algorithms frequently make implicit use of short supports — by examining a subset of the variables, they can infer support (a justifi ..."
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Cited by 2 (0 self)
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Constraint propagation is one of the key techniques in constraint programming, and a large body of work has built up around it. Specialpurpose constraint propagation algorithms frequently make implicit use of short supports — by examining a subset of the variables, they can infer support (a justification that a variablevalue pair still forms part of a solution to the constraint) for all other variables and values and save substantial work. Recently short supports have been used in general purpose propagators, and (when the constraint is amenable to short supports) speed ups of more than three orders of magnitude have been demonstrated. In this paper we present SHORTSTR2, a development of the Simple Tabular Reduction algorithm STR2+. We show that SHORTSTR2 is complementary to the existing algorithms SHORTGAC and HAGGISGAC that exploit short supports, while being much simpler. When a constraint is amenable to short supports, the short support set can be exponentially smaller than the fulllength support set. Therefore SHORTSTR2 can efficiently propagate many constraints that STR2+ cannot even load into memory. We also show that SHORTSTR2 can be combined with a simple algorithm to identify short supports from fulllength supports, to provide a superior dropin replacement for STR2+.
Global Inverse Consistency for Interactive Constraint Satisfaction ⋆
"... Abstract. Some applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inve ..."
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Abstract. Some applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multivalued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples. 1