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Sliced Table Constraints: Combining Compression and Tabular Reduction
"... Abstract. Many industrial applications require the use of table constraints (e.g., in configuration problems), sometimes of significant size. During the recent years, researchers have focused on reducing space and time complexities of this type of constraint. Static and dynamic reduction based appro ..."
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Abstract. Many industrial applications require the use of table constraints (e.g., in configuration problems), sometimes of significant size. During the recent years, researchers have focused on reducing space and time complexities of this type of constraint. Static and dynamic reduction based approaches have been proposed giving new compact representations of table constraints and effective filtering algorithms. In this paper, we study the possibility of combining both static and dynamic reduction techniques by proposing a new compressed form of table constraints based on frequent pattern detection, and exploiting it in STR (Simple Tabular Reduction).
Improving Relational Consistency Algorithms Using Dynamic Relation Partitioning
 In International Conference on Principles and Practice of Constraint Programming (CP 2014), volume LNCS 8656
, 2014
"... Abstract. Relational consistency algorithms are instrumental for solving difficult instances of Constraint Satisfaction Problems (CSPs), often allowing backtrackfree search. In this paper, we improve an algorithm for enforcing relational consistency by exploiting the property that the constraints ..."
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Abstract. Relational consistency algorithms are instrumental for solving difficult instances of Constraint Satisfaction Problems (CSPs), often allowing backtrackfree search. In this paper, we improve an algorithm for enforcing relational consistency by exploiting the property that the constraints of the dual encoding of a CSP are piecewise functional. This property allows us to partition a CSP relation into blocks of equivalent tuples at varying levels of granularity. Our new algorithm dynamically exploits those partitions. Our experiments show a significant improvement of the processing time for enforcing relational consistency.
The Smart Table Constraint
"... Abstract. Table Constraints are very useful for modeling combinatorial problems in Constraint Programming (CP). They are a universal mechanism for representing constraints, but unfortunately the size of their tables can grow exponentially with their arities. In this paper, we propose to authorize ..."
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Abstract. Table Constraints are very useful for modeling combinatorial problems in Constraint Programming (CP). They are a universal mechanism for representing constraints, but unfortunately the size of their tables can grow exponentially with their arities. In this paper, we propose to authorize entries in tables to contain simple arithmetic constraints, replacing classical tuples of values by socalled smart tuples. Smart table constraints can thus be viewed as logical combinations of those simple arithmetic constraints. This new form of tuples allows us to encode compactly many constraints, including a dozen of wellknown global constraints. We show that, under a very reasonable assumption about the acyclicity of smart tuples, a Generalized Arc Consistency algorithm of low time complexity can be devised. Our experimental results demonstrate that the smart table constraint is a highly promising general purpose tool for CP. Table constraints explicitly express the allowed combinations of values as sets of tuples, which are called tables. Table constraints can theoretically encode any kind of constraints and are amongst the most useful ones in Constraint Programming (CP). Indeed, they are often required when modeling combinatorial problems in many application fields. The design of filtering algorithms for such constraints has generated
A COMPARATIVE STUDY OF GENERALIZED ARCCONSISTENCY ALGORITHMS
, 2014
"... In this thesis, we study several algorithms for enforcing Generalized ArcConsistency (GAC), which is the most popular consistency property for solving Constraint Satisfaction Problems (CSPs) with backtrack search. The popularity of such algorithms stems from their relative low cost and effectivene ..."
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In this thesis, we study several algorithms for enforcing Generalized ArcConsistency (GAC), which is the most popular consistency property for solving Constraint Satisfaction Problems (CSPs) with backtrack search. The popularity of such algorithms stems from their relative low cost and effectiveness in improving the performance of search. Virtually all commercial and publicdomain constraint solvers include some implementation of a generic GAC algorithm. In recent years, several algorithms for enforcing GAC have been proposed in the literature that rely on increasingly complex data structures and mechanisms to improve performance. In this thesis, we study, assess, and compare a basic algorithm for generic constraints (i.e, GAC2001), new algorithms for table constraints (i.e., STR1, STR2, STR3, eSTR1, eSTR2, and STRNi), and an algorithm for constraints expressed as multivalued decision diagram (i.e., mddc). We explain the mechanisms of the above algorithms, and empirically evaluate and compare their performances. We propose a new hybrid algorithm that uses a selection criterion to combine the use of STR1 and STRNi.
Adaptive Parameterized Consistency for NonBinary CSPs by Counting Supports?
"... Abstract. Determining the appropriate level of local consistency to enforce on a given instance of a Constraint Satisfaction Problem (CSP) is not an easy task. However, selecting the right level may determine our ability to solve the problem. Adaptive parameterized consistency was recently propose ..."
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Abstract. Determining the appropriate level of local consistency to enforce on a given instance of a Constraint Satisfaction Problem (CSP) is not an easy task. However, selecting the right level may determine our ability to solve the problem. Adaptive parameterized consistency was recently proposed for binary CSPs as a strategy to dynamically select one of two local consistencies (i.e., AC and maxRPC). In this paper, we propose a similar strategy for nonbinary table constraints to select between enforcing GAC and pairwise consistency. While the former strategy approximates the supports by their rank and requires that the variables domains be ordered, our technique removes those limitations. We empirically evaluate our approach on benchmark problems to establish its advantages. 1
Generating Custom Propagators for Arbitrary Constraints
"... Constraint Programming (CP) is a proven set of techniques for solving complex combinatorial problems from a range of disciplines. The problem is specified as a set of decision variables (with finite domains) and constraints linking the variables. Local reasoning (propagation) on the constraints is c ..."
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Constraint Programming (CP) is a proven set of techniques for solving complex combinatorial problems from a range of disciplines. The problem is specified as a set of decision variables (with finite domains) and constraints linking the variables. Local reasoning (propagation) on the constraints is central to CP. Many constraints have efficient constraintspecific propagation algorithms. In this work, we generate custom propagators for constraints. These custom propagators can be very efficient, even approaching (and in some cases exceeding) the efficiency of handoptimised propagators. Given an arbitrary constraint, we show how to generate a custom propagator that establishes GAC in small polynomial time. This is done by precomputing the propagation that would be performed on every relevant subdomain. The number of relevant subdomains, and therefore the size of the generated propagator, is potentially exponential in the number and domain size of the constrained variables. The limiting factor of our approach is the size of the generated propagators. We investigate symmetry as a means of reducing that size. We exploit the symmetries of the constraint to merge symmetric parts of the generated propagator. This extends the reach of our approach to somewhat larger constraints, with a small runtime penalty. Our experimental results show that, compared with optimised implementations of the table constraint, our techniques can lead to an order of magnitude speedup. Propagation is so fast that the generated propagators compare well with handwritten carefully optimised propagators for the same constraints, and the time taken to generate a propagator is more than repaid.