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Constraints, Consistency, and Closure
 Artificial Intelligence
, 1998
"... Although the constraint satisfaction problem is NPcomplete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper, we describe a simple algebraic property which characterises all possi ..."
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Cited by 71 (14 self)
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Although the constraint satisfaction problem is NPcomplete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper, we describe a simple algebraic property which characterises all possible constraint types for which strong kconsistency is sufficient to ensure global consistency, for each k ? 2. We give a number of examples to illustrate the application of this result. 1 Introduction The constraint satisfaction problem provides a framework in which it is possible to express, in a natural way, many combinatorial problems encountered in artificial intelligence and elsewhere. The aim in a constraint satisfaction problem is to find an assignment of values to a given set of variables subject to constraints on the values which can be assigned simultaneously to certain specified subsets of variables. The constraint satisfaction problem is known to be an NPcomplete problem in ge...
A GameTheoretic Approach to Constraint Satisfaction
, 2000
"... We shed light on the connections between different approaches to constraint satisfaction by showing that the main consistency concepts used to derive tractability results for constraint satisfaction are intimately related to certain combinatorial pebble games, called the existential kpebble g ..."
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Cited by 41 (7 self)
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We shed light on the connections between different approaches to constraint satisfaction by showing that the main consistency concepts used to derive tractability results for constraint satisfaction are intimately related to certain combinatorial pebble games, called the existential kpebble games, that were originally introduced in the context of Datalog. The crucial insight relating pebble games to constraint satisfaction is that the key concept of strong kconsistency is equivalent to a condition on winning strategies for the Duplicator player in the existential kpebble game. We use this insight to show that strong kconsistency can be established if and only if the Duplicator wins the existential kpebble game. Moreover, whenever strong kconsistency can be established, one method for doing this is to first compute the largest winning strategy for the Duplicator in the existential kpebble game and then modify the original problem by augmenting it with the constraints expressed by the largest winning strategy. This basic result makes it possible to establish deeper connections between pebble games, consistency properties, and tractability of constraint satisfaction. In particular, we use existential kpebble games to introduce the concept of klocality and show that it constitutes a new tractable case of constraint satisfaction that properly extends the well known case in which establishing strong kconsistency implies global consistency.
Constraint Satisfaction and Database Theory: a Tutorial
 19th ACM Symposium on Principles of Database Systems
, 2000
"... A large class of problems in AI and other areas of computer science can be viewed as constraintsatisfaction problems. This includes problems in machine vision, belief maintenance, scheduling, temporal reasoning, type reconstruction, graph theory, and satisability. In general, the constraint satisfa ..."
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Cited by 21 (0 self)
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A large class of problems in AI and other areas of computer science can be viewed as constraintsatisfaction problems. This includes problems in machine vision, belief maintenance, scheduling, temporal reasoning, type reconstruction, graph theory, and satisability. In general, the constraint satisfactionproblem is NPcomplete, so searching for tractable cases is an active research area. It turns out that constraint satisfaction has an intimate connection with database theory: constraintsatisfaction problems can be recast as database problems and database problems can be recast as constraintsatisfaction problems. In this tutorial, I will cover the fundamentals of constraints saisfaction and describe its intimate relationship with database theory from various perspectives. 1 Introduction Since the early 1970s, researchers in articial intelligence have investigated a class of combinatorial problems that became known as constraintsatisfaction problems (CSP). The input to such a pro...
The State of SAT
, 2005
"... The papers in this special issue originated at SAT 2001, the Fourth International Symposium on the Theory and Applications of Satisfiability Testing. This foreword reviews the current state of satisfiability testing and places the papers in this issue in context. Key words: Boolean satisfiability, c ..."
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Cited by 19 (2 self)
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The papers in this special issue originated at SAT 2001, the Fourth International Symposium on the Theory and Applications of Satisfiability Testing. This foreword reviews the current state of satisfiability testing and places the papers in this issue in context. Key words: Boolean satisfiability, complexity, challenge problems.
Ten challenges redux: Recent progress in propositional reasoning and search
 In Proceedings of CP ’03
, 2003
"... Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1 ..."
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Cited by 18 (1 self)
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Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1
Reasoning on Interval and Pointbased Disjunctive Metric Constraints in Temporal Contexts
 Journal of Artificial Intelligence Research
, 2000
"... We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defineslabeled disjunctive metric pointbased co ..."
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Cited by 17 (1 self)
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We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled temporal algebra defineslabeled disjunctive metric pointbased constraints, where each disjunct in each input disjunctive constraint is univocally associated to a label. Reasoning algorithms manage labeled constraints, associated label lists, and sets of mutually inconsistent disjuncts. These algorithms guarantee consistency and obtain a minimal network. Additionally, constraints can be organized in a hierarchy of alternative temporal contexts. Therefore, we can reason on contextdependent disjunctive metric constraints on intervals and points. Moreover, the model is able to represent nonbinary constraints, such that logical dependencies on disjuncts in constraints can be handled. The computational cost of reasoning algorithms is exponential in ac...
Modelling and Solving Employee Timetabling Problems
 Annals of Mathematics and Artificial Intelligence
, 2002
"... Employee timetabling is the operation of assigning employees to tasks in a set of shifts during a xed period of time, typically a week. We present a general de nition of employee timetabling problems (ETPs) that captures many realworld problem formulations and includes complex constraints. The ..."
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Cited by 15 (4 self)
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Employee timetabling is the operation of assigning employees to tasks in a set of shifts during a xed period of time, typically a week. We present a general de nition of employee timetabling problems (ETPs) that captures many realworld problem formulations and includes complex constraints. The proposed model of ETPs can be represented in a tabular form that is both intuitive and ecient for constraint representation and processing. The constraint networks of ETPs include nonbinary constraints and are dicult to formulate in terms of simple constraint solvers. We investigate the use of local search techniques for solving ETPs. In particular, we propose several versions of hillclimbing that make use of a novel search space that includes also partial assignments.
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 13 (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.
Temporal Reasoning and Constraint Programming  A Survey
 CWI Quarterly
, 1998
"... Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . ..."
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Cited by 8 (1 self)
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Contents 1 Introduction 6 1.1 Temporal Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Constraint problems and constraint satisfaction . . . . . . 7 1.2.2 Algorithms to solve constraints . . . . . . . . . . . . . . . 9 1.3 Temporal reasoning and Constraint Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Temporal Reasoning with metric information . . . . . . . 14 1.3.2 Qualitative approach based on Allen's interval algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Mixed approaches . . . . . . . . . . . . . . . . . . . . . . 15 2 Temporal Reasoning and Constraint Programming 16 2.1 Temporal Constraints with metric information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 A first order language . . . . . . . . . . . . . . . . . . . . 16 2.1.2 The original Temporal Constraint Problem . .
Consistency and set intersection, in
 Proceedings of International Joint Conference on Artificial Intelligence 2003
"... We propose a new framework to study properties of consistency in a Constraint Network from the perspective of properties of set intersection. Our framework comes with a proof schema which gives a generic way of lifting a set intersection property to one on consistency. Various well known results can ..."
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Cited by 5 (4 self)
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We propose a new framework to study properties of consistency in a Constraint Network from the perspective of properties of set intersection. Our framework comes with a proof schema which gives a generic way of lifting a set intersection property to one on consistency. Various well known results can be derived with this framework. More importantly, we use the framework to obtain a number of new results. We identify a new class of tree convex constraints where local consistency ensures global consistency. Another result is that in a network of arbitrary constraints, local consistency implies global consistency whenever there arc certain mtight constraints. The most interesting result is that when the constraint on every pair of variables is properly mtight in an arbitrary network, global consistency can be achieved by enforcing relational m=1consistency. These results significantly improve our understanding of convex and tight constraints. This demonstrates that our framework is a promising and powerful tool for studying consistency. 1