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Valued constraint satisfaction problems: Hard and easy problems
 IJCAI’95: PROCEEDINGS INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1995
"... In order to deal with overconstrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathematical operator (+, max...) to aggregate constraint violat ..."
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Cited by 331 (42 self)
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In order to deal with overconstrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathematical operator (+, max...) to aggregate constraint violations. In this paper, we consider a simple algebraic framework, related to Partial Constraint Satisfaction, which subsumes most of these proposals and use it to characterize existing proposals in terms of rationality and computational complexity. We exhibit simple relationships between these proposals, try to
Adopt: asynchronous distributed constraint optimization with quality guarantees
 ARTIFICIAL INTELLIGENCE LABORATORY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2005
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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 206 (26 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.
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 114 (28 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].
Arc Consistency for Soft Constraints
 Artificial Intelligence
"... . Traditionally, local consistency is dened as a relaxation of consistency which can be checked in polynomial time. It is accompanied by a corresponding \ltering" or \enforcing" algorithm that computes in polynomial time, and from any given CSP, an equivalent unique CSP which satises t ..."
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Cited by 91 (27 self)
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. Traditionally, local consistency is dened as a relaxation of consistency which can be checked in polynomial time. It is accompanied by a corresponding \ltering" or \enforcing" algorithm that computes in polynomial time, and from any given CSP, an equivalent unique CSP which satises the local consistency property. The question whether the notion of local consistency can be extended to soft constraint frameworks has been addressed by several papers, in several settings [4, 14, 12]. The main positive conclusion of these works is that the notion of local consistency can be extended to soft constraints frameworks which rely on an idempotent violation combination operator. However, the question whether this can be done for non idempotent operators as eg, in the MaxCSP problem, is not clear and has lead to several dierent notions of arc consistency [14, 16, 1, 11, 10]. Each of these proposals lacks several of the original properties of local consistency. In this paper, we...
Radio Link Frequency Assignment
 Constraints
, 1999
"... The problem of radio frequency assignment is to provide communication channels from limited spectral resources whilst keeping to a minimum the interference suffered by those whishing to communicate in a given radio communication network. This problem is a combinatorial (NPhard) optimization problem ..."
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Cited by 70 (11 self)
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The problem of radio frequency assignment is to provide communication channels from limited spectral resources whilst keeping to a minimum the interference suffered by those whishing to communicate in a given radio communication network. This problem is a combinatorial (NPhard) optimization problem. In 1993, the CELAR (the French "Centre d'Electronique de l'Armement") built a suite of simplified versions of Radio Link Frequency Assignment Problems (RLFAP) starting from data on a real network (Roisnel 93). Initially designed for assessing the performances of several Constraint Logic Programming languages, these benchmarks have been made available to the public in the framework of the European EUCLID project CALMA (Combinatorial Algorithms for Military Applications).
Soft Concurrent Constraint Programming
, 2001
"... . Soft constraints extend classical constraints to represent multiple consistency levels, and thus provide a way to express preferences, fuzziness, and uncertainty. While there are many soft constraint solving algorithms, even distributed ones, by now there seems to be no concurrent programming fram ..."
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Cited by 59 (34 self)
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. Soft constraints extend classical constraints to represent multiple consistency levels, and thus provide a way to express preferences, fuzziness, and uncertainty. While there are many soft constraint solving algorithms, even distributed ones, by now there seems to be no concurrent programming framework where soft constraints can be handled. In this paper we show how the classical concurrent constraint (cc) programming framework can work with soft constraints, and we also propose an extension of cc languages which can use soft constraints to prune and direct the search for a solution. We believe that this new programming paradigm, called soft cc (scc), can be very useful in many webrelated scenarios. In fact, the language level allows web agents to express their interaction and negotiation protocols, and also to post their requests in terms of preferences, and the underlying soft constraint solver can nd an agreement among the agents even if their requests are incompatible. 1
Semiringbased Constraint Logic Programming: Syntax and Semantics
, 2001
"... this paper, more simply, soft constraint problems. ..."
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Cited by 56 (28 self)
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this paper, more simply, soft constraint problems.
Russian Doll Search for Solving Constraint Optimization Problems
 Proceedings AAAI
, 1996
"... If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor qua ..."
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Cited by 55 (12 self)
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If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminish...
Semiringbased CSPs and Valued CSPs: Basic Properties and Comparison
, 1996
"... . We introduce 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. We then compare the two approaches and we discu ..."
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Cited by 47 (10 self)
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. We introduce 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. We then compare the two approaches and we discuss the relationship between them. 1 Introduction Classical constraint satisfaction problems (CSPs) [19, 17] are a very expressive and natural formalism to specify many kinds of reallife problems. In fact, problems ranging from map coloring, vision, robotics, jobshop scheduling, VLSI design, etc., can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [8, 9, 18, 16, 19]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent reallife scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the abilit...