Results 1  10
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20
Circuit Complexity and Decompositions of Global Constraints
 In 21st Int. Joint Conf. on AI
, 2009
"... We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a spe ..."
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Cited by 21 (5 self)
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We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint. 1
Decompositions of All Different, Global Cardinality and Related Constraints
"... We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide ..."
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Cited by 18 (9 self)
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We show that some common and important global constraints like ALLDIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudoBoolean solver. 1
A Generalized ArcConsistency Algorithm for a Class of Counting Constraints
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... This paper introduces the SEQ BIN metaconstraint with a polytime algorithm achieving generalized arcconsistency. SEQ BIN can be used for encoding counting constraints such as CHANGE, SMOOTH, or INCREASING NVALUE. For all of them the time and space complexity is linear in the sum of domain sizes, w ..."
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Cited by 6 (3 self)
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This paper introduces the SEQ BIN metaconstraint with a polytime algorithm achieving generalized arcconsistency. SEQ BIN can be used for encoding counting constraints such as CHANGE, SMOOTH, or INCREASING NVALUE. For all of them the time and space complexity is linear in the sum of domain sizes, which improves or equals the best known results of the literature.
Decomposition of the NVALUE constraint
"... Abstract. We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a much greater space complexity. This suggests that t ..."
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Cited by 5 (0 self)
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Abstract. We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a much greater space complexity. This suggests that the benefit of a global propagator may often not be in saving time but in saving space. Our other theoretical contribution is to show for the first time that range consistency can be enforced on NVALUE with the same worstcase time complexity as bound consistency. Finally, the decompositions we study are readily encoded as linear inequalities. We are therefore able to use them in integer linear programs. 1
Open Contractible Global Constraints
"... Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. However, in general, filtering that is ..."
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Cited by 5 (0 self)
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Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a simple characterization, called contractibility, of the constraints where filtering remains sound when the constraint is open. With this characterization we can easily determine whether a constraint is contractible or not. In the latter case, we can use it to derive the strongest contractible approximation to the constraint. We demonstrate how specific algorithms for some closed contractible constraints are easily adapted to open constraints. 1
On matrices, automata, and double counting
 In CPAIOR’2010, volume 6140 of LNCS
, 2010
"... Abstract Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finitestate automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double coun ..."
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Cited by 4 (1 self)
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Abstract Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finitestate automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances. 1
The increasing nvalue Constraint
 In Proc. CPAIOR
, 2010
"... Abstract. This paper introduces the Increasing Nvalue constraint, which restricts the number of distinct values assigned to a sequence of variables so that each variable in the sequence is less than or equal to its successor. This constraint is a specialization of the Nvalue constraint, motivated by ..."
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Cited by 4 (2 self)
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Abstract. This paper introduces the Increasing Nvalue constraint, which restricts the number of distinct values assigned to a sequence of variables so that each variable in the sequence is less than or equal to its successor. This constraint is a specialization of the Nvalue constraint, motivated by symmetry breaking. Propagating the Nvalue constraint is known as an NPhard problem. However, we show that the chain of non strict inequalities on the variables makes the problem polynomial. We propose an algorithm achieving generalized arcconsistency in O(ΣDi) time, where ΣDi is the sum of domain sizes. This algorithm is an improvement of filtering algorithms obtained by the automatonbased or the Slidebased reformulations. We evaluate our constraint on a resource allocation problem. 1
Including Soft Global Constraints in DCOPs
, 2012
"... In the centralized context, global constraints have been essential for the advancement of constraint reasoning. In this paper we propose to include soft global constraints in distributed constraint optimization problems (DCOPs). Looking for efficiency, we study possible decompositions of global cons ..."
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Cited by 3 (0 self)
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In the centralized context, global constraints have been essential for the advancement of constraint reasoning. In this paper we propose to include soft global constraints in distributed constraint optimization problems (DCOPs). Looking for efficiency, we study possible decompositions of global constraints, including the use of extra variables. We extend the distributed search algorithm BnBADOPT + to support these representations of global constraints. In addition, we explore the relation of global constraints with soft local consistency in DCOPs, in particular for the generalized soft arc consistency (GAC) level. We include specific propagators for some wellknown soft global constraints. Finally, we provide empirical results on several benchmarks.
The SEQBIN Constraint Revisited
, 2012
"... We revisit the SEQBIN constraint [1]. This metaconstraint subsumes a number of important global constraints like CHANGE [2], SMOOTH [3] and INCREASINGNVALUE [4]. We show that the previously proposed filtering algorithm for SEQBIN has two drawbacks even under strong restrictions: it does not detect ..."
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Cited by 3 (0 self)
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We revisit the SEQBIN constraint [1]. This metaconstraint subsumes a number of important global constraints like CHANGE [2], SMOOTH [3] and INCREASINGNVALUE [4]. We show that the previously proposed filtering algorithm for SEQBIN has two drawbacks even under strong restrictions: it does not detect bounds disentailment and it is not idempotent. We identify the cause for these problems, and propose a new propagator that overcomes both issues. Our algorithm is based on a connection to the problem of finding a path of a given cost in a restricted npartite graph. Our propagator enforces domain consistency in O(nd 2) and, for special cases of SEQBIN that include CHANGE,SMOOTH and INCREASINGNVALUE in O(nd) time.
An Optimal Arc Consistency Algorithm for a Particular Case of Sequence Constraint
"... Abstract. The ATMOSTSEQCARD constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints ATMOST u on each subsequence of size q. This constraint is useful in carsequencing and crewrostering problems. In [21], two algorithms designed for the AM ..."
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Cited by 2 (2 self)
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Abstract. The ATMOSTSEQCARD constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints ATMOST u on each subsequence of size q. This constraint is useful in carsequencing and crewrostering problems. In [21], two algorithms designed for the AMONGSEQ constraint were adapted to this constraint with an O(2qn) and O(n3) worst case time complexity, respectively. In [10], another algorithm similarly adaptable to filter the ATMOSTSEQCARD constraint with a time complexity of O(n2) was proposed. In this paper, we introduce an algorithm for achieving arc consistency on the ATMOSTSEQCARD constraint with an O(n) (hence optimal) worst case time complexity. Next, we show that this algorithm can be easily modified to achieve arc consistency on some extensions of this constraint. In particular, the conjunction of a set ofm ATMOSTSEQCARD constraints sharing the same scope can be filtered in O(nm). We then empirically study the efficiency of our propagator on instances of the carsequencing and crewrostering problems. 1