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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 77 (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
Cp(graph): Introducing a graph computation domain in constraint programming
 In CP2005 Proceedings
, 2005
"... Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new co ..."
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Cited by 53 (12 self)
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Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain variables as well as constraints over these variables and their propagators. These constraints are subdivided into kernel constraints and additional constraints formulated as networks of kernel constraints. For some of these constraints a dedicated global constraint and its associated propagator are sketched. CP(Graph) is integrated with finite domain and finite sets computation domains, allowing the combining of constraints of these domains with graph constraints. A prototype of CP(Graph) built over finite domains and finite sets in Oz is presented. And we show that a problem of biochemical network analysis can be very simply described and solved within CP(Graph). 1
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 35 (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
General symmetry breaking constraints
 In: 12th International Conference on Principles and Practices of Constraint Programming (CP2006), SpringerVerlag
, 2006
"... Abstract. We present some general constraints for breaking symmetries in constraint satisfaction problems. These constraints can be used to break symmetries acting on variables, values, or both. We also consider symmetry breaking constraints to deal with conditional symmetries, and symmetries acting ..."
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Cited by 28 (16 self)
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Abstract. We present some general constraints for breaking symmetries in constraint satisfaction problems. These constraints can be used to break symmetries acting on variables, values, or both. We also consider symmetry breaking constraints to deal with conditional symmetries, and symmetries acting on set and other types of variables. 1
Symmetry in constraint programming
 Handbook of Constraint Programming
, 2006
"... Symmetry in constraints has always been important but in recent years has become a major research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this problem has been solved, with a numbe ..."
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Cited by 26 (3 self)
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Symmetry in constraints has always been important but in recent years has become a major research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this problem has been solved, with a number of different techniques. As we write, research remains very active for two reasons. First, there are many difficulties in the practical application of the techniques that are known for symmetry exclusion, and overcoming these remain important research problems. Second, the successes achieved in the area so far have encouraged researchers to find new ways to exploit symmetry. In this chapter we cover both these issues, and the details of the symmetry exclusion methods that have been conceived. Figure 10.1: The solution to the puzzle of finding a chess position containing nine queens and a king of each colour, with the rule that no piece is on the same line (row, column or diagonal) as any queen of the opposite colour. Up to symmetry, the solution is unique. 330 10. Symmetry in Constraint Programming To illustrate what we mean by symmetry, we consider the chess puzzle shown in Figure 10.1. The solution to this puzzle is unique “up to symmetry ” [115], but what do
Global Constraint Catalogue: Past, Present and Future
, 2006
"... The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area. ..."
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Cited by 26 (2 self)
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The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area.
Symmetry breaking using value precedence
 In: Proceedings of the 17th ECAI, European Conference on Artificial Intelligence, IOS
, 2006
"... Abstract. We present a comprehensive study of the use of valueprecedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is bothefficient and effective at breaking symmetry. We then extend value precedence to deal with a number o ..."
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Cited by 24 (22 self)
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Abstract. We present a comprehensive study of the use of valueprecedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is bothefficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreathvalue and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries. 1 INTRODUCTION Symmetry is an important aspect of many search problems. Symmetry occurs naturally in many problems (e.g. if we have two identical
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