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22
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
On the Computation of Local Interchangeability In Discrete Constraint Satisfaction Problems
, 1998
"... In [4], Freuder defines several types of interchange ability to capture the equivalence among the values of a variable in a discrete constraint satisfaction prob lem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedu ..."
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Cited by 37 (8 self)
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In [4], Freuder defines several types of interchange ability to capture the equivalence among the values of a variable in a discrete constraint satisfaction prob lem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedure for computing a weak form of local interchangeability. Second, we show that the modified procedure can be used to generate a conjunctire decomposition of the CSP by localizing, in the CSP, independent subproblems. Third, for the case of constraints of mutual exclusion, we show that locally interchangeable values can be computed in a straightforward manner, and that the only possible type of local interchangeability is the one that induces locally independent subproblems. Finally, we give hints on how to exploit these results in practice, establish a lattice that relates some types of interchangeability, and identify directions for future research.
A Constraint Satisfaction Framework for Decision Under Uncertainty
 In Proc. of the 11th Int. Conf. on Uncertainty in Artificial Intelligence
, 1995
"... The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal with some decisions problems under uncertainty. This extensio ..."
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Cited by 27 (1 self)
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The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal with some decisions problems under uncertainty. This extension relies on a differentiation between the agentcontrollable decision variables and the uncontrollable parameters whose values depend on the occurrenceof uncertain events. The uncertainty on the values of the parameters is assumed to be given under the form of a probability distribution. Two algorithms are given, for computing respectively decisions solving the problem with a maximal probability, and conditional decisions mapping the largest possible amount of possible cases to actual decisions. 1 Introduction Decision making is primarily a matter of choosing between alternatives that most commonly are expressed implicitly. Thus solving a decision problem amounts to generate the option(s) t...
Using Symmetry of Global Constraints to Speed up the Resolution of Constraint Satisfaction Problems
 in Workshop on Non Binary Constraints, ECAI98
, 1998
"... Abstract. Symmetry in constraint satisfaction problems (CSP) can be used to either compute only a subset of the total solution set, or to prune branches of the search tree. However, detecting symmetry in general is a difficult task. In this paper, we address the problem of detecting and exploiting a ..."
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Cited by 19 (0 self)
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Abstract. Symmetry in constraint satisfaction problems (CSP) can be used to either compute only a subset of the total solution set, or to prune branches of the search tree. However, detecting symmetry in general is a difficult task. In this paper, we address the problem of detecting and exploiting a particular class of symmetry called intensional permutability, which is based on the notion of interchangeability between variables and can be detected with a very small overhead. This kind of symmetry is detected by collecting information on symmetrical properties of individual constraints. This method works particularly well on problems designed using global constraints. We show how intensional permutability dramatically reduces the search tree for some problems. We propose a simple method to exploit it, which can be implemented as a lightweight extension to most resolution algorithms based on backtracking. We illustrate the method on several symmetrical problems, such as a classical layout problem and the pigeonhole problem, stated with a global constraint. Finally, we extend the method to symmetries involving groups of variables. 1
Certainty closure: A framework for reliable constraint reasoning with uncertainty
 in Proc. CP’03
, 2003
"... Abstract Constraint problems with incomplete or erroneous data are often simplified to tractable deterministic models, or modified using error correction methods, with the aim of seeking a solution. However, this can lead us to solve the wrong problem because of the approximations made. Such an ou ..."
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Cited by 19 (4 self)
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Abstract Constraint problems with incomplete or erroneous data are often simplified to tractable deterministic models, or modified using error correction methods, with the aim of seeking a solution. However, this can lead us to solve the wrong problem because of the approximations made. Such an outcome is of little help to a user who expects the right problem to be tackled and reliable information returned. The certainty closure framework we present aims to provide the user with reliable insight by: (1) enclosing the uncertainty using what is known for sure about the data, to guarantee that the true problem is contained in the model so described, (2) deriving a closure, a set of possible solutions to the uncertain constraint problem. In this paper we first demonstrate the benefits of reliable constraint reasoning on two different case studies, and then generalise our approaches into a formal framework. 1
Constraint weighting local search for constraint satisfaction
, 2000
"... One of the challenges for the constraint satisfaction community has been to develop an automated approach to solving Constraint Satisfaction Problems (CSPs) rather than creating specific algorithms for specific problems. Much of this work has concentrated on the development and improvement of genera ..."
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Cited by 9 (3 self)
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One of the challenges for the constraint satisfaction community has been to develop an automated approach to solving Constraint Satisfaction Problems (CSPs) rather than creating specific algorithms for specific problems. Much of this work has concentrated on the development and improvement of general purpose backtracking techniques. However, the success of relatively simple local search techniques on larger satisfiability problems [Selman et al. 1992] and CSPs such as the nqueens [Minton et al. 1992] has caused interest in applying local search to constraint satisfaction. In this thesis we look at the usefulness of constraint weighting as a local search technique for constraint satisfaction. The work is based on the clause weighting ideas of Selman and Kautz [1993] and Morris [1993] and applies, evaluates and extends these ideas from the satisfiability domain to the more general domain of CSPs. Specifically, the contributions of the thesis are: The introduction of a local search taxonomy. We examine the various better known local search techniques and recognise four basic strategies: restart, randomness, memory and weighting.
Blocksolve: a BottomUp Approach for Solving Quantified CSPs
 In Proceedings of CP2006
, 2006
"... Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solv ..."
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Cited by 8 (0 self)
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Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solve it. In this paper we propose BlockSolve, an algorithm for solving QCSPs that factorizes computations made in branches of the search tree. Instead of following the order of the variables in the quantification sequence, our technique searches for combinations of values for existential variables at the bottom of the tree that will work for (several) values of universal variables earlier in the sequence. An experimental study shows the good performance of BlockSolve compared to a state of the art QCSP solver. 1
Exploiting problem structure as a search heuristic
 International Journal of Modern Physics C
, 1995
"... Recent empirical and theoretical studies have shown that simple parameters characterizing constraint satisfaction problems predict whether they have a solution and the cost to solve them, on average. This paper examines the effectiveness of using these predictions as a heuristic for solving the grap ..."
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Cited by 8 (1 self)
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Recent empirical and theoretical studies have shown that simple parameters characterizing constraint satisfaction problems predict whether they have a solution and the cost to solve them, on average. This paper examines the effectiveness of using these predictions as a heuristic for solving the graph coloring problem. Specifically, by adding some global information on the consequences of various choices, the use of these parameters can reduce the search required to find a solution. Current limitations of this approach, due to the high variance associated with the predictions, are also presented. More generally, observations of universal behaviors analogous to physical phase transitions can be applied to improve search methods. 1
An interval constraint branching scheme for lattice domains
 Journal of Universal Computer Science
"... Abstract This paper presents a branching schema for the solving of a wide range of interval constraint satisfaction problems defined on any domain of computation, finite or infinite, provided the domain forms a lattice. After a formal definition of the branching schema, useful and interesting proper ..."
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Cited by 2 (1 self)
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Abstract This paper presents a branching schema for the solving of a wide range of interval constraint satisfaction problems defined on any domain of computation, finite or infinite, provided the domain forms a lattice. After a formal definition of the branching schema, useful and interesting properties, satisfied by all instances of the schema, are presented. Examples are then used to illustrate how a range of operational behaviors can be modelled by means of different schema instantiations. It is shown how the operational procedures of many constraint systems (including cooperative systems) can be viewed as instances of this branching schema. Basic directives to adapt this schema to solving constraint optimization problems are also provided.
Domain Decomposition for Parallel Resolution of Constraint Satisfaction Problems with OpenMP
 In Proceedings of the Second European Workshop on OpenMP
, 2000
"... Many problems in computer science, especially in Artificial Intelligence, can be represented as constraint satisfaction problems (CSP). For example, scene labeling in computer vision involves testing possible interpretation of objects against relation rules. Other constraint satisfaction problems ..."
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Cited by 2 (0 self)
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Many problems in computer science, especially in Artificial Intelligence, can be represented as constraint satisfaction problems (CSP). For example, scene labeling in computer vision involves testing possible interpretation of objects against relation rules. Other constraint satisfaction problems include theorem proving, scheduling, expert systems. These problems are typically NPComplete because they require extensive searches to find a solution and the basic search algorithm is the naive Backtracking strategy. In order to improve its performances different approaches have been explored: filtering strategies, heuristics for search algorithms, decomposition methods. Although parallelization seems to be a good candidate to obtain further practical improvements the research in this direction is fewly developed. In this paper we explore the benefit of a domain decomposition strategy for parallel CSP resolution. Mainly we solve in parallel the different subproblems resulting from the decomposition step on a shared memory architecture with an OpenMP library. All the experiments were realized with the Sillicon Graphics Origin2000 parallel machine.