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The Complexity of Global Constraints
, 2004
"... We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, ..."
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Cited by 82 (23 self)
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We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, metaconstraints like the cardinality constraint, and learning nogoods.
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 76 (5 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
Deriving Filtering Algorithms from Constraint Checkers
 Principles and Practice of Constraint Programming (CP’2004), volume 3258 of LNCS
, 2004
"... Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction ..."
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Cited by 51 (11 self)
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Abstract. This reportdeals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in ¦ , where ¦ is the number of variables of the corresponding global constraint. By reformulating the automaton as a conjunction of signature and transition constraints we show how to systematically obtain a filtering algorithm. Under some restrictions on the signature and transition constraints this filtering algorithm achieves arcconsistency. 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 a filtering algorithm for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution. Keywords: Constraint Programming,
Filtering algorithms for the NValue constraint
 In Proceedings CPAIOR’05
, 2005
"... Abstract. The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NPhard. We show that computing even the lower bound on the number of values is NPhard. We therefore study different approximation h ..."
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Cited by 34 (10 self)
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Abstract. The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NPhard. We show that computing even the lower bound on the number of values is NPhard. We therefore study different approximation heuristics for this problem. We introduce three new methods for computing a lower bound on the number of values. The first two are based on the maximum independent set problem and are incomparable to a previous approach based on intervals. The last method is a linear relaxation of the problem. This gives a tighter lower bound than all other methods, but at a greater asymptotic cost. 1 Introduction The NValue constraint counts the number of distinct values used by a vectorof variables. It is a generalization of the widely used AllDifferent constraint[12]. It was introduced in [4] to model a musical playlist configuration problem so
A New MultiResource cumulatives Constraint with Negative Heights
, 2001
"... This paper presents a new s cumulative constraint which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling ..."
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Cited by 30 (3 self)
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This paper presents a new s cumulative constraint which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way new scheduling and planning problems. The introduction of negative heights has forced us to come up with new propagation algorithms and to revisit existing ones. The first propagation algorithm is derived from an idea called sweep which is extensively used in computational geometry; the second algorithm is based on a combination of sweep and constructive disjunction, while the last is a generalization of task intervals to this new context. A reallife timetabling problem originally motivated this constraint which was implemented within the SICStus finite domain solver and evaluated against different problem patterns.
GLOBAL CONSTRAINTS AND FILTERING ALGORITHMS
"... Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algor ..."
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Cited by 22 (1 self)
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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Overconstrained problems are also mentioned and global soft constraints are introduced.
The Range and Roots Constraints: Specifying Counting and Occurrence Problems
 In IJCAI
, 2005
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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 ..."
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Cited by 10 (3 self)
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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 reformulation. Under some restrictions on the signature and transition constraints, this reformulation maintains arcconsistency. 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 reformulation for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution.
The Complexity of Reasoning with Global Constraints
 Constraints
, 2006
"... Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or nonbinary) constraints, the cost of such propagation may be much greater than the quad ..."
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Cited by 10 (1 self)
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Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or nonbinary) constraints, the cost of such propagation may be much greater than the quadratic cost for binary constraints. We therefore study the computational complexity of reasoning with global constraints. We first characterise a number of important questions related to constraint propagation. We show that such questions are intractable in general, and identify dependencies between the tractability and intractability of the different questions. We then demonstrate how the tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when constraints can be safely generalized, when decomposing constraints will reduce the amount of pruning, and when combining constraints is tractable.
Kernels for Global Constraints
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever b ..."
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Cited by 8 (6 self)
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Bessière et al. (AAAI’08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixedparameter tractable in k – the number of holes in domains – whenever bound consistency can be enforced in polynomial time; this applies to the global constraints ATMOSTNVALUE and EXTENDED GLOBAL CARDINALITY (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for ATMOSTNVALUE constraints admits a linear time reduction to an equivalent instance on O(k2) variables and domain values. This small kernel can be used to speed up the complete propagation of NVALUE constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.