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31
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 (8 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...
Partition Search for Nonbinary Constraint Satisfaction
 Information Sciences
, 2007
"... Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Anal ..."
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Cited by 18 (0 self)
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Previous algorithms for unrestricted constraint satisfaction use reduction search, which inferentially removes values from domains in order to prune the backtrack search tree. This paper introduces partition search, which uses an efficient join mechanism instead of removing values from domains. Analytical prediction of quantitative performance of partition search appears to be intractable and evaluation therefore has to be by experimental comparison with reduction search algorithms that represent the state of the art. Instead of working only with available reduction search algorithms, this paper introduces enhancements such as semijoin reduction preprocessing using Bloom filtering.
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 14 (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 9 (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.
Trading Off Solution Quality for Faster Computation in DCOP Search Algorithms ∗
"... 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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Cited by 8 (3 self)
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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
Distributed Gibbs: A MemoryBounded SamplingBased DCOP Algorithm
"... Researchers have used distributed constraint optimization problems (DCOPs) to model various multiagent coordination and resource allocation problems. Very recently, Ottens et al. proposed a promising new approach to solve DCOPs that is based on confidence bounds via their Distributed UCT (DUCT) sam ..."
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Cited by 6 (6 self)
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Researchers have used distributed constraint optimization problems (DCOPs) to model various multiagent coordination and resource allocation problems. Very recently, Ottens et al. proposed a promising new approach to solve DCOPs that is based on confidence bounds via their Distributed UCT (DUCT) samplingbased algorithm. Unfortunately, its memory requirement per agent is exponential in the number of agents in the problem, which prohibits it from scaling up to large problems. Thus, in this paper, we introduce a new samplingbased DCOP algorithm called Distributed Gibbs, whose memory requirements per agent is linear in the number of agents in the problem. Additionally, we show empirically that our algorithm is able to find solutions that are better than DUCT; and computationally, our algorithm runs faster than DUCT as well as solve some large problems that DUCT failed to solve due to memory limitations.
C.: Solving Difficult CSPs with Relational Neighborhood Inverse Consistency
 In: 25 th AAAI Conference on Artificial Intelligence (AAAI
, 2011
"... Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In thi ..."
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Cited by 5 (3 self)
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Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational Neighborhood Inverse Consistency (RNIC) as a local consistency property that operates on the dual graph of a nonbinary CSP. We describe and characterize a practical algorithm for enforcing it. We argue that defining RNIC on the dual graph unveils unsuspected opportunities to reduce the computational cost of our algorithm and increase its filtering effectiveness. We show how to achieve those effects by modifying the topology of the dual graph, yielding new variations the RNIC property. We also introduce an adaptive strategy to automatically select the appropriate property to enforce given the connectivity of the dual graph. We integrate the resulting techniques as full lookahead strategies in a backtrack search procedure for solving CSPs, and demonstrate the effectiveness of our approach for solving known difficult benchmark problems. 1
Partial Enumeration and Curvature Regularization
"... Energies with highorder nonsubmodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NPhard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all p ..."
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Cited by 4 (2 self)
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Energies with highorder nonsubmodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NPhard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. This partial enumeration technique reduces complex highorder energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRWS. Our approach outperforms a number of existing stateoftheart algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. Our main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach. 1 1.
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 4 (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.
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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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