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34
Combining Qualitative and Quantitative Constraints in Temporal Reasoning
 Artificial Intelligence
, 1996
"... This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the ..."
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Cited by 139 (0 self)
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This paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information. This model allows the representation and processing of many types of constraints discussed in the literature to date, including metric constraints (restricting the distance between time points) and qualitative, disjunctive constraints (specifying the relative position of temporal objects). Reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques, such as backtracking and path consistency. New classes of tractable problems are characterized, involving qualitative networks augmented by quantitative domain constraints, some of which can be solved in polynomial time using arc and path consistency. This work was supported in part by grants from the Air Force Office of Scientific Research, AFOSR 900136, and the National Science Foundation, IRI 8815522...
Arc Consistency for General Constraint Networks: Preliminary Results
, 1997
"... Constraint networks are used more and more to solve combinatorial problems in reallife applications. Much activity is concentrated on improving the efficiency of finding a solution in a constraint network (the constraint satisfaction problem, CSP). Particularly, arc consistency caught many research ..."
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Cited by 127 (15 self)
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Constraint networks are used more and more to solve combinatorial problems in reallife applications. Much activity is concentrated on improving the efficiency of finding a solution in a constraint network (the constraint satisfaction problem, CSP). Particularly, arc consistency caught many researchers' attention, involving the discovery of a large number of algorithms. And, for the last two years, it has been shown that maintaining arc consistency during search is a worthwhile approach. However, results on CSPs and on arc consistency are almost always limited to binary constraint networks. The CSP is no longer an academic problem, and it is time to deal with nonbinary CSPs, as widely required in real world constraint solvers. This paper proposes a general schema to implement arc consistency on constraints of any arity when no specific algorithm is known. A first instantiation of the schema is presented here, which deals with constraints given by a predicate, by the set of forbidden c...
Local and global relational consistency
 THEORETICAL COMPUTER SCIENCE
, 1997
"... Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consiste ..."
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Cited by 61 (15 self)
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Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consistency, which we characterize as variablebased. We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new definition in characterizing relationships between properties of constraint networks and the level of local consistency needed to ensure global consistency.
Temporal Constraint Reasoning with Preferences
, 2001
"... A number of reasoning problems involving the manipulation of temporal information can be viewed as implicitly inducing an ordering of decisions involving time (associated with durations or orderings of events) on the basis of preferences. For example, a pair of events might be constrained to o ..."
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Cited by 58 (9 self)
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A number of reasoning problems involving the manipulation of temporal information can be viewed as implicitly inducing an ordering of decisions involving time (associated with durations or orderings of events) on the basis of preferences. For example, a pair of events might be constrained to occur in a certain order, and, in addition, it might be preferable that the delay between them be as large, or as small, as possible. This paper explores problems in which a set of temporal constraints is specified, each with preference criteria for making local decisions about the events involved in the constraint. A reasoner must infer a complete solution to the problem such that, to the extent possible, these local preferences are met in the best way. Constraintbased temporal reasoning is generalized to allow for reasoning about temporal preferences, and the complexity of the resulting formalism is examined. While in general such problems are NPcomplete, some restrictions on the shape of the preference functions, and on the structure of the set of preference values, can be enforced to achieve tractability. In these cases, a generalization of a singlesource shortest path algorithm can be used to compute a globally preferred solution in polynomial time.
Consistency Techniques for Continuous Constraints
 Constraints
, 1996
"... We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constrai ..."
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Cited by 56 (7 self)
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We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.
Constraint tightness and looseness versus local and global consistency
 Journal of the ACM
, 1997
"... Constraint networks are a simple representation and reasoning framework with diverse applications. In this paper, weidentify two new complementary properties on the restrictiveness of the constraints in a network constraint tightness and constraint loosenessand we show their usefulness for estimat ..."
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Cited by 25 (2 self)
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Constraint networks are a simple representation and reasoning framework with diverse applications. In this paper, weidentify two new complementary properties on the restrictiveness of the constraints in a network constraint tightness and constraint loosenessand we show their usefulness for estimating the level of local consistency needed to ensure global consistency, and for estimating the level of local consistency present ina network. In particular, we present a su cient condition, based on constraint tightness and the level of local consistency, that guarantees that a solution can be found in a backtrackfree manner. The condition can be useful in applications where a knowledge base will be queried over and over and the preprocessing costs can be amortized over many queries. We also present a su cient condition for local consistency, based on constraint looseness, that is straightforward and inexpensive to determine. The condition can be used to estimate the level of local consistency of a network. This in turn can be used in deciding whether it would be useful to preprocess the network before a backtracking search, and in deciding which local consistency conditions, if any, still need to be enforced if we want to ensure that a solution can be found in a backtrackfree manner. Two denitions of local consistency are employed in characterizing the conditions: the traditional variablebased notion and a recently introduced de nition of local consistency called relational consistency 1. 1 Some of the results reported in this paper have previously appeared at KR94 [28] and 1 1
Local Consistency on Conjunctions of Constraints
"... Constraint networks are used more and more to solve combinatorial problems in reallife applications. As pointed out in [BR97], this success requires dealing with nonbinary constraints, which are widely needed in real world constraint solvers. Since arc consistency is a fundamental piece of reasonin ..."
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Cited by 19 (0 self)
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Constraint networks are used more and more to solve combinatorial problems in reallife applications. As pointed out in [BR97], this success requires dealing with nonbinary constraints, which are widely needed in real world constraint solvers. Since arc consistency is a fundamental piece of reasoning that seems to be of great help during search for solutions, it is important to have efficient arc consistency algorithms for nonbinary constraints. In [BR97], a first step has been done, resulting in a general schema for arc consistency on any kind of constraints, and in instantiations of the schema to handle the more general nonbinary constraints, i.e., those given as a predicate or as a set of allowed/forbidden combinations of values. In this paper, we extend that work by proposing an efficient way to compute local consistency on conjunctions of constraints (called conjunctive consistency). We then use this notion to improve arc consistency processing on two practical cases, embedding co...
Tradeoffs in the complexity of backdoor detection
 In Principles and Practice of Constraint Programming  CP 2007
, 2007
"... Abstract. There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are “easily ” identifiable, while others are of interest because they capture key aspects of stateoft ..."
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Cited by 15 (6 self)
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Abstract. There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are “easily ” identifiable, while others are of interest because they capture key aspects of stateoftheart constraint solvers. In particular, it was recently shown that the problem of identifying a strong Horn or 2CNFbackdoor can be solved by exploiting equivalence with deletion backdoors, and is NPcomplete. We prove that strong backdoor identification becomes harder than NP (unless NP=coNP) as soon as the inconsequential sounding feature of empty clause detection (present in all modern SAT solvers) is added. More interestingly, in practice such a feature as well as polynomial time constraint propagation mechanisms often lead to much smaller backdoor sets. In fact, despite the worstcase complexity results for strong backdoor detection, we show that SatzRand is remarkably good at finding small strong backdoors on a range of experimental domains. Our results suggest that structural notions explored for designing efficient algorithms for combinatorial problems should capture both statically and dynamically identifiable properties. 1
Domain filtering consistencies for nonbinary constraints
 ARTIFICIAL INTELLIGENCE
, 2008
"... In nonbinary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering ..."
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Cited by 15 (5 self)
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In nonbinary constraint satisfaction problems, the study of local consistencies that only prune values from domains has so far been largely limited to generalized arc consistency or weaker local consistency properties. This is in contrast with binary constraints where numerous such domain filtering consistencies have been proposed. In this paper we present a detailed theoretical, algorithmic and empirical study of domain filtering consistencies for nonbinary problems. We study three domain filtering consistencies that are inspired by corresponding variable based domain filtering consistencies for binary problems. These consistencies are stronger than generalized arc consistency, but weaker than pairwise consistency, which is a strong consistency that removes tuples from constraint relations. Among other theoretical results, and contrary to expectations, we prove that these new consistencies do not reduce to the variable based definitions of their counterparts on binary constraints. We propose a number of algorithms to achieve the three consistencies. One of these algorithms has a time complexity comparable to that for generalized arc consistency despite performing more pruning. Experiments demonstrate that our new consistencies are promising as they can be more efficient than generalized arc consistency on certain nonbinary problems.
SemiAutomatic Modeling by Constraint Acquisition
 In Francesca Rossi, editor, International Conference on Principles and Practice of Constraint Programming, number 2833 in LNCS
, 2003
"... Constraint programming is a technology which is now widely used to solve combinatorial problems in industrial applications. However, using it requires considerable knowledge and expertise in the field of constraint reasoning. ..."
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Cited by 8 (2 self)
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Constraint programming is a technology which is now widely used to solve combinatorial problems in industrial applications. However, using it requires considerable knowledge and expertise in the field of constraint reasoning.