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Valued constraint satisfaction problems: Hard and easy problems
 IJCAI’95: Proceedings International Joint Conference on Artificial Intelligence
, 1995
"... tschiexOtoulouse.inra.fr fargierOirit.fr verfailOcert.fr 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 mathema ..."
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Cited by 287 (40 self)
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tschiexOtoulouse.inra.fr fargierOirit.fr verfailOcert.fr 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
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 102 (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].
Solution reuse in dynamic constraint satisfaction problems
 In Proceedings of the 12th National Conference on Artificial Intelligence
, 1994
"... Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or other agents in the framework of a distributed system. In this context, computing a new solution from s ..."
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Cited by 87 (6 self)
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Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or other agents in the framework of a distributed system. In this context, computing a new solution from scratch after each problem change is possible, but has two important drawbacks: inefficiency and instability of the successive solutions. In this paper, we propose a method for reusing any previous solution and producing a new one by local changes on the previous one. First we give the key idea and the corresponding algorithm. Then we establish
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 41 (9 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...
MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems
 In Proceedings of the Second International Conference on Principles and Practice of Constraint Programming
, 1996
"... . In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often le ..."
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Cited by 40 (3 self)
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. In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FCCBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks. 1 Introducti...
Lazy Arc Consistency
 In Proceedings of the Thirteenth National Conference on Artificial Intelligence
, 1996
"... Arc consistency filtering is widely used in the framework of binary constraint satisfaction problems: with a low complexity, inconsistency may be detected and domains are filtered. In this paper, we show that when detecting inconsistency is the objective, a systematic domain filtering is useless and ..."
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Cited by 20 (0 self)
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Arc consistency filtering is widely used in the framework of binary constraint satisfaction problems: with a low complexity, inconsistency may be detected and domains are filtered. In this paper, we show that when detecting inconsistency is the objective, a systematic domain filtering is useless and a lazy approach is more adequate. Whereas usual arc consistency algorithms produce the maximum arc consistent subdomain, when it exists, we propose a method, called LAC7 , which only looks for any arc consistent subdomain. The algorithm is then extended to provide the additional service of locating one variable with a minimum domain cardinality in the maximum arc consistent subdomain, without necessarily computing all domain sizes. Finally, we compare traditional AC enforcing and lazy AC enforcing using several benchmark problems, both randomly generated CSP and real life problems. The Constraint Satisfaction Problem (CSP) framework is increasingly used to represent and solve numerous O...
Extracting constraint satisfaction subproblems
 In Proceedings of the 14 th International Joint Conference on Artificial Intelligence (IJCAI’95
, 1995
"... Given a subproblem, S, of a constraint satisfaction problem, we can decompose the problem into a set of disjoint subproblems one of which will be S. This decomposition permits exploitation of problemspecific metaknowledge, a priori or acquired knowledge, about S. If we know that S is unsolvable, fo ..."
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Cited by 20 (0 self)
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Given a subproblem, S, of a constraint satisfaction problem, we can decompose the problem into a set of disjoint subproblems one of which will be S. This decomposition permits exploitation of problemspecific metaknowledge, a priori or acquired knowledge, about S. If we know that S is unsolvable, for example, the decomposition permits us to extract and then discard S, restricting the search for a solution to the remaining subproblems. A variety of potential uses for the decomposition method are discussed. A specific method that dynamically discards failed subproblems during forward checking search is described, and its utility demonstrated experimentally.
Compilation for Critically Constrained Knowledge Bases
 In Proc. of the 13 th National Conference on Artificial Intelligence (AAAI’96
, 1996
"... We show that many "critically constrained" Random 3SAT knowledge bases (KBs) can be compiled into disjunctive normal form easily by using a variant of the "DavisPutnam" proof procedure. From these compiled KBs we can answer all queries about entailment of conjunctive normal formulas, also easily  ..."
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Cited by 16 (0 self)
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We show that many "critically constrained" Random 3SAT knowledge bases (KBs) can be compiled into disjunctive normal form easily by using a variant of the "DavisPutnam" proof procedure. From these compiled KBs we can answer all queries about entailment of conjunctive normal formulas, also easily  compared to a "bruteforce " approach to approximate knowledge compilation into unit clauses for the same KBs. We exploit this fact to develop an aggressive hybrid approach which attempts to compile a KB exactly until a given resource limit is reached, then falls back to approximate compilation into unit clauses. The resulting approach handles all of the critically constrained Random 3SAT KBs with average savings of an order of magnitude over the bruteforce approach. Introduction Consider the task of reasoning from a propositional knowledge base (KB) F which is expressed as a conjunctive normal formula (CNF). We are given other, query CNFs Q 1 ; Q 2 ; : : : ; QN and asked, for each Q i ,...
Dynamic Backtracking for Dynamic Constraint Satisfaction Problems
 In Proceedings of the ECAI94 Workshop on Constraint Satisfaction Issues Raised by Practical Applications
, 1994
"... Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or the other agents in the framework of a distributed system. The notion of dynamic CSP (DCSP) has been in ..."
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Cited by 14 (2 self)
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Many AI problems can be modeled as constraint satisfaction problems (CSP), but many of them are actually dynamic: the set of constraints to consider evolves because of the environment, the user or the other agents in the framework of a distributed system. The notion of dynamic CSP (DCSP) has been introduced to represent them. In spite of its name, the recent Dynamic Backtracking algorithm proposed in (Ginsberg 1993) does not solve dynamic CSPs, but static ones. But its nogood recording and backtracking mechanisms are very interesting in the DCSP framework. In this paper, we propose an extension of this algorithm which provides the user with explanations in case of inconsistency and allows dynamic CSPs to be dealt with very efficiently. After presenting the Dynamic Backtracking algorithm, its extension and how to use it in the DCSP framework, we present and discuss some experimental results. Dynamic backtracking In (Ginsberg 1993), Matthew L. Ginsberg proposed a new algorithm for solv...
Constrained Decision Diagrams
, 2005
"... A general nary constraint is usually represented explicitly as a set of its solution tuples, which may need exponential space. In this paper, we introduce a new representation for general nary constraints called Constrained Decision Diagram (CDD). CDD generalizes BDDstyle representations and the ..."
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Cited by 11 (3 self)
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A general nary constraint is usually represented explicitly as a set of its solution tuples, which may need exponential space. In this paper, we introduce a new representation for general nary constraints called Constrained Decision Diagram (CDD). CDD generalizes BDDstyle representations and the main feature is that it combines constraint reasoning/consistency techniques with a compact data structure. We present an application of CDD for recording all solutions of a conjunction of constraints. Instead of an explicit representation, we can implicitly encode the solutions by means of constraint propagation. Our experiments confirm the scalability and demonstrate that CDDs can drastically reduce the space needed over explicit and ZBDD representations.