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Algorithms for Constraint Satisfaction Problems: A Survey
 AI MAGAZINE
, 1992
"... 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. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic ..."
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Cited by 427 (0 self)
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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. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.
SemiringBased Constraint Satisfaction and Optimization
 JOURNAL OF THE ACM
, 1997
"... We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be asso ..."
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Cited by 194 (24 self)
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We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (1 and 3) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.
Closure Properties of Constraints
 Journal of the ACM
, 1997
"... Many combinatorial search problems can be expressed as `constraint satisfaction problems', and this class of problems is known to be NPcomplete in general. In this paper we investigate the subclasses which arise from restricting the possible constraint types. We first show that any set of cons ..."
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Cited by 158 (16 self)
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Many combinatorial search problems can be expressed as `constraint satisfaction problems', and this class of problems is known to be NPcomplete in general. In this paper we investigate the subclasses which arise from restricting the possible constraint types. We first show that any set of constraints which does not give rise to an NPcomplete class of problems must satisfy a certain type of algebraic closure condition. We then investigate all the different possible forms of this algebraic closure property, and establish which of these are sufficient to ensure tractability. As examples, we show that all known classes of tractable constraints over finite domains can be characterised by such an algebraic closure property. Finally, we describe a simple computational procedure which can be used to determine the closure properties of a given set of constraints. This procedure involves solving a particular constraint satisfaction problem, which we call an `indicator problem'. Keywords: Cons...
Semiringbased CSPs and Valued CSPs: Frameworks, Properties, and Comparison
 Constraints
, 1999
"... In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two ..."
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Cited by 111 (27 self)
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In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two approaches, we show how to pass from one to the other one, and we discuss when this is possible. The two frameworks have been independently introduced in [2], [3] and [35].
Constraint Solving over Semirings
 in IJCAI
, 1995
"... We introduce a general framework for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated to each tuple o ..."
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Cited by 109 (37 self)
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We introduce a general framework for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated to each tuple of values of the variable domain, and the two semiring operations (+ and x) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that some conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving schemes, thus allowing one both to formally justify many informally taken choices in existing schemes, and to prove that the local consistency techniques can be used also in newly defined schemes. 1
The Essence of Constraint Propagation
 CWI QUARTERLY VOLUME 11 (2&3) 1998, PP. 215 { 248
, 1998
"... We show that several constraint propagation algorithms (also called (local) consistency, consistency enforcing, Waltz, ltering or narrowing algorithms) are instances of algorithms that deal with chaotic iteration. To this end we propose a simple abstract framework that allows us to classify and comp ..."
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Cited by 104 (6 self)
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We show that several constraint propagation algorithms (also called (local) consistency, consistency enforcing, Waltz, ltering or narrowing algorithms) are instances of algorithms that deal with chaotic iteration. To this end we propose a simple abstract framework that allows us to classify and compare these algorithms and to establish in a uniform way their basic properties.
On the Equivalence of Constraint Satisfaction Problems
 In Proceedings of the 9th European Conference on Artificial Intelligence
, 1990
"... A solution of a Constraint Satisfaction Problem (CSP) is an assignment of values to all its variables such that all its constraints are satisfied. Usually two CSPs are considered equivalent if they have the same solution set. We find this definition limiting, and develop a more general definition ba ..."
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Cited by 96 (0 self)
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A solution of a Constraint Satisfaction Problem (CSP) is an assignment of values to all its variables such that all its constraints are satisfied. Usually two CSPs are considered equivalent if they have the same solution set. We find this definition limiting, and develop a more general definition based on the concept of mutual reducibility. In this extended scheme it is reasonable to consider a pair of CSPs equivalent even if they have different solutions. The basic idea behind the extended scheme is that two CSPs can be considered equivalent whenever they contain the same "amount of information", i.e. whenever it is possible to obtain the solution of one of them from the solution of the other one, and viceversa. In this way, both constraint and variable redundancy are allowed in CSPs belonging to the same equivalence class. As an example of the usefulness of this new notion of equivalence, we formally prove that binary and nonbinary CSPs are equivalent (in the new sense). Such a pro...
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 68 (5 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
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 63 (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...
Ccpi: A constraintbased language for specifying service level agreements
 In ESOP, volume 4421 of LNCS
, 2007
"... Abstract. Service Level Agreements are a key issue in Service Oriented Computing. SLA contracts specify client requirements and service guarantees, with emphasis on Quality of Service (cost, performance, availability, etc.). In this work we propose a simple model of contracts for QoS and SLAs that a ..."
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Cited by 62 (5 self)
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Abstract. Service Level Agreements are a key issue in Service Oriented Computing. SLA contracts specify client requirements and service guarantees, with emphasis on Quality of Service (cost, performance, availability, etc.). In this work we propose a simple model of contracts for QoS and SLAs that also allows to study mechanisms for resource allocation and for joining different SLA requirements. Our language combines two basic programming paradigms: namepassing calculi and concurrent constraint programming (cc programming). Specifically, we extend cc programming by adding synchronous communication and by providing a treatment of names in terms of restriction and structural axioms closer to nominal calculi than to variables with existential quantification. In the resulting framework, SLA requirements are constraints that can be generated either by a single party or by the synchronisation of two agents. Moreover, restricting the scope of names allows for local stores of constraints, which may become global as a consequence of synchronisations. Our approach relies on a system of named constraints that equip classical constraints with a suitable algebraic structure providing a richer mechanism of constraint combination. We give reductionpreserving translations of both cc programming and the calculus of explicit fusions. 1