Results 1  10
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27
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 22 (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 17 (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
The parameterized complexity of global constraints
 In Proceedings of AAAI 2008, AAAI Conference on Artificial Intelligence
, 2008
"... We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixedparameter tractable and which are easy to compute. This tract ..."
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Cited by 16 (4 self)
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We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixedparameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has a strong backdoor of bounded size. This strong backdoor is often a cycle cutset. We also show that parameterized complexity can be used to study other aspects of constraint programming like symmetry breaking. For instance, we prove that value symmetry is fixedparameter tractable to break in the number of symmetries. Finally, we argue that parameterized complexity can be used to derive results about the approximability of constraint propagation.
A large neighbourhood search approach to the multiactivity shift scheduling problem
 In TR
, 2007
"... 2500 chemin de Polytechnique Abstract. The challenge in shift scheduling lies in the construction of a set of work shifts, which are subject to specific regulations, in order to cover fluctuating staff demands. This problem becomes harder when multiskill employees can perform many different activit ..."
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Cited by 11 (2 self)
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2500 chemin de Polytechnique Abstract. The challenge in shift scheduling lies in the construction of a set of work shifts, which are subject to specific regulations, in order to cover fluctuating staff demands. This problem becomes harder when multiskill employees can perform many different activities during the same shift. In this paper, we show how formal languages (such as regular and contextfree languages) can be enhanced and used to model the complex regulations of the shift construction problem. From these languages we can derive specialized graph structures that can be searched efficiently. The overall shift scheduling problem can then be solved using a Large Neighbourhood Search. These approaches are able to return near optimal solution on traditional single activity problems and they scale well on large instances containing up to 10 activities. 1.
Efficient contextfree grammar constraints
 IN: AAAI
, 2008
"... With the introduction of constraints based on finite automata a new line of research has opened where constraints are based on formal languages. Recently, constraints based on grammars higher up in the Chomsky hierarchy were introduced. We devise a time and spaceefficient incremental arcconsisten ..."
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Cited by 10 (3 self)
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With the introduction of constraints based on finite automata a new line of research has opened where constraints are based on formal languages. Recently, constraints based on grammars higher up in the Chomsky hierarchy were introduced. We devise a time and spaceefficient incremental arcconsistency algorithm for contextfree grammars. Particularly, we show how to filter a sequence of monotonically tightening problems in cubic time and quadratic space. Experiments on a scheduling problem show orders of magnitude improvements in time and space consumption.
Restricted Global Grammar Constraints.
"... We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous contextfree grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar. We also ..."
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Cited by 10 (2 self)
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We investigate the global GRAMMAR constraint over restricted classes of context free grammars like deterministic and unambiguous contextfree grammars. We show that detecting disentailment for the GRAMMAR constraint in these cases is as hard as parsing an unrestricted context free grammar. We also consider the class of linear grammars and give a propagator that runs in quadratic time. Finally, to demonstrate the use of linear grammars, we show that a weighted linear GRAMMAR constraint can efficiently encode the EDITDISTANCE constraint, and a conjunction of the EDITDISTANCE constraint and the REGULAR constraint.
Global constraints: A survey
 IN
, 2011
"... Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP because they exploit the specific structure of each constraint. This chapter is an overview of these two techniques. A collection of the most frequently u ..."
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Cited by 7 (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 because they exploit the specific structure of each constraint. This chapter is an overview of these two techniques. A collection of the most frequently used global constraints is given and some filtering algorithms are detailed. In addition, we try to identify how filtering algorithms can be designed. At last, we identify some problems that deserve to be addressed in the future.
The Weighted CFG Constraint
 In 5th Int. Conf. on Integration of AI and OR Techniques in CP (CPAIOR
"... Abstract. We introduce the weighted CFG constraint and propose a propagation algorithm that enforces domain consistency in O(n 3 G) time. We show that this algorithm can be decomposed into a set of primitive arithmetic constraints without hindering propagation. 1 ..."
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Cited by 6 (4 self)
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Abstract. We introduce the weighted CFG constraint and propose a propagation algorithm that enforces domain consistency in O(n 3 G) time. We show that this algorithm can be decomposed into a set of primitive arithmetic constraints without hindering propagation. 1
Two Encodings of DNNF Theories
"... Abstract. The paper presents two new compilation schemes of Decomposable Negation Normal Form (DNNF) theories into Conjunctive Normal Form (CNF) and Linear Integer Programming (MIP), respectively. We prove that the encodings have useful properties such as unit propagation on the CNF formula achieves ..."
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Cited by 5 (0 self)
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Abstract. The paper presents two new compilation schemes of Decomposable Negation Normal Form (DNNF) theories into Conjunctive Normal Form (CNF) and Linear Integer Programming (MIP), respectively. We prove that the encodings have useful properties such as unit propagation on the CNF formula achieves domain consistency on the DNNF theory. The approach is evaluated empirically on random as well as realworld CSPproblems. 1
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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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