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39
SLIDE: A Useful Special Case of the CARDPATH Constraint
 In 18th European Conf. on AI
"... Abstract. We study the CARDPATH constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CARDPATH where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CA ..."
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Cited by 19 (6 self)
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Abstract. We study the CARDPATH constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CARDPATH where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CARDPATH itself. We consider how to propagate SLIDE and provide a complete propagator for CARDPATH. Since propagation is NPhard in general, we identify special cases where propagation takes polynomial time. Our experiments demonstrate that using SLIDE to encode global constraints can be as efficient and effective as specialised propagators. 1
FlowBased Propagators for the SEQUENCE and Related Global Constraints
, 2008
"... We propose new filtering algorithms for the SEQUENCE constraint and some extensions of the SEQUENCE constraint based on network flows. We enforce domain consistency on the SEQUENCE constraint in O(n 2) time down a branch of the search tree. This improves upon the best existing domain consistency al ..."
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Cited by 16 (3 self)
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We propose new filtering algorithms for the SEQUENCE constraint and some extensions of the SEQUENCE constraint based on network flows. We enforce domain consistency on the SEQUENCE constraint in O(n 2) time down a branch of the search tree. This improves upon the best existing domain consistency algorithm by a factor of O(log n). The flows used in these algorithms are derived from a linear program. Some of them differ from the flows used to propagate global constraints like GCC since the domains of the variables are encoded as costs on the edges rather than capacities. Such flows are efficient for maintaining bounds consistency over large domains and may be useful for other global constraints.
The slide metaconstraint
"... We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide ..."
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Cited by 15 (3 self)
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We study the Slide metaconstraint. This slides a constraint down one or more sequences of variables. We show that Slide can be used to encode and propagate a wide range of global constraints. We consider a number of extensions including sliding down sequences of set variables, and combining Slide with a global cardinality constraint. We also show how to propagate Slide. Our experiments demonstrate that using Slide to encode constraints can be just as efficient and effective as using specialized propagators.
Reformulating global constraints: the Slide and Regular constraints
, 2007
"... Global constraints are useful for modelling and reasoning about realworld combinatorial problems. Unfortunately, developing propagation algorithms to reason about global constraints efficiently and effectively is usually a difficult and complex process. In this paper, we show that reformulation ma ..."
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Cited by 9 (1 self)
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Global constraints are useful for modelling and reasoning about realworld combinatorial problems. Unfortunately, developing propagation algorithms to reason about global constraints efficiently and effectively is usually a difficult and complex process. In this paper, we show that reformulation may be helpful in building such propagators. We consider both hard and soft forms of two powerful global constraints, Slide and Regular. These global constraints are useful to represent a wide range of problems like rostering and scheduling where we have a sequence of decision variables and some constraint that holds along the sequence. We show that the different forms of Slide and Regular can all be reformulated as each other. We also show that reformulation is an effective method to incorporate such global constraints within an existing constraint toolkit. Finally, this study provides insight into the close relationship between these two important global constraints.
Sequencing and counting with the multicostregular constraint
 In Lecture notes in computer science, 6th international conference on integration of AI and OR techniques in
, 2009
"... Abstract. This paper introduces a global constraint encapsulating a regular constraint together with several cumulative costs. It is motivated in the context of personnel scheduling problems, where a schedule meets patterns and occurrence requirements which are intricately bound. The optimization pr ..."
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Cited by 9 (1 self)
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Abstract. This paper introduces a global constraint encapsulating a regular constraint together with several cumulative costs. It is motivated in the context of personnel scheduling problems, where a schedule meets patterns and occurrence requirements which are intricately bound. The optimization problem underlying the multicostregular constraint is NPhard but it admits an efficient Lagrangian relaxation. Hence, we propose a filtering based on this relaxation. The expressiveness and the efficiency of this new constraint is experimented on personnel scheduling benchmark instances with standard work regulations. The comparative empirical results show how multicostregular can significantly outperform a decomposed model with regular and globalcardinality constraints. 1
Towards Efficient Consistency Enforcement for Global Constraints in Weighted Constraint Satisfaction
"... Powerful consistency techniques, such as AC* and FDAC*, have been developed for Weighted Constraint Satisfaction Problems (WCSPs) to reduce the space in solution search, but are restricted to only unary and binary constraints. On the other hand, van Hoeve et al. developed efficient graphbased algor ..."
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Cited by 8 (1 self)
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Powerful consistency techniques, such as AC* and FDAC*, have been developed for Weighted Constraint Satisfaction Problems (WCSPs) to reduce the space in solution search, but are restricted to only unary and binary constraints. On the other hand, van Hoeve et al. developed efficient graphbased algorithms for handling soft constraints as classical constraint optimization problems. We prove that naively incorporating van Hoeve’s method into the WCSP framework can enforce a strong form of ∅Inverse Consistency, which can prune infeasible values and deduce good lower bound estimates. We further show how Van Hoeve’s method can be modified so as to handle cost projection and extension to maintain the stronger AC* and FDAC* generalized for nonbinary constraints. Using the soft allDifferent constraint as a testbed, preliminary results demonstrate that our proposal gives improvements up to an order of magnitude both in terms of time and pruning.
Open constraints in a closed world
 In Proceedings of CPAIOR 2006, volume 3990 of LNCS
, 2006
"... Abstract. We study domain filtering algorithms for open constraints, i.e., constraints that are not a priori defined on specific sets of variables. We present an efficient filtering algorithm, achieving setdomain consistency, for open global cardinality constraints. We extend this result to conjunc ..."
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Cited by 6 (2 self)
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Abstract. We study domain filtering algorithms for open constraints, i.e., constraints that are not a priori defined on specific sets of variables. We present an efficient filtering algorithm, achieving setdomain consistency, for open global cardinality constraints. We extend this result to conjunctions of them, in case they are defined on disjoint sets of variables. We also analyze the case when the sets of variables may overlap. As establishing setdomain consistency is NPcomplete in that case, we propose a weaker, though efficient, filtering algorithm instead. Finally, we extend our results to conjunctions of similar open constraints. 1
Improved algorithm for the soft global cardinality constraint
 IN PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS, CPAIOR06, VOL. LNCS 3990
, 2006
"... We propose two algorithms achieving generalized arc consistency for the soft global cardinality constraint with variablebased violation and with valuebased violation. They are based on graph theory and their complexity is O( nm) where n is the number of variables and m is the sum of the cardinalit ..."
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Cited by 5 (1 self)
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We propose two algorithms achieving generalized arc consistency for the soft global cardinality constraint with variablebased violation and with valuebased violation. They are based on graph theory and their complexity is O( nm) where n is the number of variables and m is the sum of the cardinalities of the domains. They improve previous algorithms that ran respectively in O(n(m+n log n)) and O((n + k)(m + n log n)) where k is the cardinality of the union of the domains.