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Dual Modelling of Permutation and Injection Problems
 Journal of Artificial Intelligence Research
, 2004
"... When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many ..."
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Cited by 30 (9 self)
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general...
Local Consistencies in SAT
 In Proc. SAT2003
, 2003
"... We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem. ..."
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Cited by 11 (1 self)
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We introduce some new mappings of constraint satisfaction problems into propositional satisability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational karc consistency on the original problem.
Methods for Interactive Constraint Satisfaction
, 2003
"... A constraint satisfaction problem involves the assignment of values to variables subject to a set of constraints. A large variety of problems in artificial intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. In many applications, o ..."
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Cited by 7 (0 self)
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A constraint satisfaction problem involves the assignment of values to variables subject to a set of constraints. A large variety of problems in artificial intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. In many applications, one example being product configuration, user interaction is required to find a solution. The topic of this thesis is algorithmic methods for solving constraint satisfaction problems interactively. A number of fundamental operations, which form the core of an interactive constraint solver, are identified and described formally. The decision version of the constraint satisfaction problem is NPcomplete, so a method of offline compilation is proposed to circumvent this intractability and achieve short response times for these fundamental operations.
Constraint Relaxation Techniques to Aid the Reuse of Knowledge Bases and Problem Solvers
"... Effective reuse of knowledge bases requires the identification of plausible combinations of both problem solvers and knowledge bases, which can be an expensive task. Can we identify impossible combinations quickly? The capabilities of combinations can be represented using constraints, and we propos ..."
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Cited by 3 (1 self)
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Effective reuse of knowledge bases requires the identification of plausible combinations of both problem solvers and knowledge bases, which can be an expensive task. Can we identify impossible combinations quickly? The capabilities of combinations can be represented using constraints, and we propose using constraint relaxation to help eliminate impossible combinations. If a relaxed constraint representation of a combination is inconsistent then we know that the original combination is inconsistent as well. We examine different relaxation strategies based on constraint graph properties, and we show that removing constraints of low tightness is an efficient strategy which is also simple to implement.
Tight and tractable reformulations for uncertain CSPs
 In Proc. of CPā04 Workshop on Modelling and Reformulating Constraint Satisfaction Problems
, 2004
"... Abstract Various extensions of the CSP framework exist to address illdefined, realworld optimisation problems. One extension, the uncertain CSP (UCSP) tackles the aspect of data errors and incompleteness by ensuring that the problem is faithfully represented with what is known for sure about the d ..."
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Cited by 2 (1 self)
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Abstract Various extensions of the CSP framework exist to address illdefined, realworld optimisation problems. One extension, the uncertain CSP (UCSP) tackles the aspect of data errors and incompleteness by ensuring that the problem is faithfully represented with what is known for sure about the data, and by seeking reliable solutions that do not approximate such uncertainties. The extended model has a great impact on the solving complexity. For instance, by introducing bounded interval coefficients, the default representation of an arithmetic linear constraint is of degree 2. A challenge lies in determining constraint classes that allow one to reformulate the UCSP model such that polynomial algorithms exist. In this paper we present two novel sufficient conditions, built on algebraic properties of constraints, that ensure a tractable reformulation exists. We give an algorithm to test for the conditions for binary constraints, and demonstrate as instances some previously identified practical UCSP reformulations. 1
Encoding Table Constraints in CLP(FD) Based on Pairwise AC
"... Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime r ..."
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Cited by 2 (2 self)
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Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime removal of unsupported values. For nary constraints, we propose pairwise arc consistency (AC), which ensures that each value has a support in the domain of every related variable. Pairwise AC does not require introducing new problem variables as done in binarization methods and allows for compact representation of constraints. Nevertheless, pairwise AC is weaker than general arc consistency (GAC) in terms of pruning power and requires a final check when a constraint becomes ground. To remedy this weakness, we propose adopting early checks when constraints are sufficiently instantiated. Our experimentation shows that pairwise AC with early checking is as effective as GAC for positive constraints. 1
Refutation Analysis for Constraint Satisfaction Problems
, 2007
"... Good heuristics have long been credited as some of the most important components of constraint satisfaction search algorithms. Understanding their behaviour has been the subject of a significant number of both theoretical and empirical research papers, yet from a practical standpoint, questions abou ..."
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Cited by 1 (0 self)
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Good heuristics have long been credited as some of the most important components of constraint satisfaction search algorithms. Understanding their behaviour has been the subject of a significant number of both theoretical and empirical research papers, yet from a practical standpoint, questions about certain important performance characteristics remained unanswered. For example, what is the smallest possible refutation of an insoluble search tree? Are heavytailed runtime distributions encountered for a given search algorithm inherently heavytailed? Refutations oftentimes involve only a small subset of the uninstantiated variables. Could simply reordering those variables lead to better refutations? Are those variables special? This dissertation introduces a methodology for finding some of those answers through a type of empirical analysis never attempted before. At the core of the research presented here lies an algorithm that takes on the computationally expensive task of obtaining optimal refutations for all the insol
Trading Off Solution Quality for Faster Computation in DCOP Search Algorithms ā
"... Distributed Constraint Optimization (DCOP) is a key technique for solving agent coordination problems. Because finding costminimal DCOP solutions is NPhard, it is important to develop mechanisms for DCOP search algorithms that trade off their solution costs for smaller runtimes. However, existing ..."
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Distributed Constraint Optimization (DCOP) is a key technique for solving agent coordination problems. Because finding costminimal DCOP solutions is NPhard, it is important to develop mechanisms for DCOP search algorithms that trade off their solution costs for smaller runtimes. However, existing tradeoff mechanisms do not provide relative error bounds. In this paper, we introduce three tradeoff mechanisms that provide such bounds, namely the Relative Error Mechanism, the Uniformly Weighted Heuristics Mechanism and the NonUniformly Weighted Heuristics Mechanism, for two DCOP algorithms, namely ADOPT and BnBADOPT. Our experimental results show that the Relative Error Mechanism generally dominates the other two tradeoff mechanisms for ADOPT and the Uniformly Weighted Heuristics Mechanism generally dominates the other two tradeoff mechanisms for BnBADOPT. 1
ControllerAgent based approach for Solving Distributed Constraint Problem
"... Abstract. The interesting domain of constraint programming has been studied for years. Using Constraint Satisfaction Problem in association with MultiAgent System has emerged the research in a new field known as Distributed Constraint Satisfaction Problem (DCSP). Many algorithms are proposed to sol ..."
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Abstract. The interesting domain of constraint programming has been studied for years. Using Constraint Satisfaction Problem in association with MultiAgent System has emerged the research in a new field known as Distributed Constraint Satisfaction Problem (DCSP). Many algorithms are proposed to solve DCSP. Inspired from ABT algorithm, we introduce in this paper our algorithm for solving DCSP where we divide agents in the system into two groups: Variables ā and Controller Agents, which allow reformulating of different interagent communication algorithm in our framework. This division allows the separation between the constraints verification and other functions of agents. The proposed algorithm is not only capable of treating binary constraints; it can be used easily in order to treat nonbinary constraints. This facility gives also the possibility of grouping constraints in order to form a set of quasiindependent subproblems. These subproblems may be interconnected by some common variables. The instantiation of these variables can be done by negotiation in order to separate the subproblems into totally independent ones. 12 1