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A unified theory of structural tractability for constraint satisfaction and spread cut decomposition
 In Proceedings of the 19th International Joint Conference on Artificial Intelligence
, 2005
"... In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified addition ..."
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Cited by 19 (2 self)
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In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of decomposition, which we call a spread cut. We show that discovery of width k spreadcut decompositions is tractable for each k, and that the spread cut decomposition strongly generalize all existing decompositions except hypertrees. Finally we exhibit a family of hypergraphs Hn, for n = 1, 2, 3..., where the width of the best hypertree decomposition of each Hn is at least 3n, but the width of the best spreadcut decomposition is at most 2n. 1
The complexity of weighted boolean #CSP
, 2007
"... This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of nonnegative functions that may be used to assign weights to the configurations (feasibl ..."
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Cited by 16 (6 self)
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This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of nonnegative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1valued functions. We show that the partition function, i.e. the sum of the weights of all configurations, can be computed in polynomial time if either (1) every function in F is of “product type”, or (2) every function in F is “pure affine”. For every other fixed set F, computing the partition function is FP #Pcomplete.
Contractor Programming
 Artificial Intelligence
"... Abstract. This paper describes a solver programming method, called contractor programming, that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restr ..."
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Cited by 15 (8 self)
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Abstract. This paper describes a solver programming method, called contractor programming, that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restricting users to choose among a list of fixed strategies. Our first contribution is to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available. Programming consists in applying operators (intersection, composition, etc.) on algorithms called contractors that are somehow similar to propagators. Second, many problems with real variables cannot be cast as the search for vectors simultaneously satisfying the set of constraints, but a large variety of different outputs may be demanded from a set of constraints (e.g., a paving with boxes inside and outside of the solution set). These outputs can actually be viewed as the result of different contractors working concurrently on the same search space, with a bisection procedure intervening in case of deadlock. Such algorithms (which are not strictly speaking solvers) will be made easy to build thanks to a new branch & prune system, called paver. Thus, this paper gives a way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms. The contractor formalism and the paver system are the two contributions. The approach is motivated and justified through different cases of study. An implementation of this framework named Quimper is also presented. 1
An approximation trichotomy for Boolean #CSP
, 2007
"... We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in constraints. If every relation in the constraint language is ..."
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Cited by 13 (4 self)
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We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in constraints. If every relation in the constraint language is affine then the number of satisfying assignments can be exactly counted in polynomial time. Otherwise, if every relation in the constraint language is in the coclone IM2 from Post’s lattice, then the problem of counting satisfying assignments is complete with respect to approximationpreserving reductions in the complexity class #RHΠ1. This means that the problem of approximately counting satisfying assignments of such a CSP instance is equivalent in complexity to several other known counting problems, including the problem of approximately counting the number of independent sets in a bipartite graph. For every other fixed constraint language, the problem is complete for #P with respect to approximationpreserving reductions, meaning that there is no fully polynomial randomised approximation scheme for counting satisfying assignments unless NP=RP. 1
OWL Datatypes: Design and Implementation
"... Abstract. We analyze the datatype system of OWL and OWL 2, and discuss certain nontrivial consequences of its definition, such as the extensibility of the set of supported datatypes and complexity of reasoning. We also argue that certain datatypes from the list of normative datatypes in the current ..."
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Cited by 8 (4 self)
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Abstract. We analyze the datatype system of OWL and OWL 2, and discuss certain nontrivial consequences of its definition, such as the extensibility of the set of supported datatypes and complexity of reasoning. We also argue that certain datatypes from the list of normative datatypes in the current OWL 2 Working Draft are inappropriate and should be replaced with different ones. Finally, we present an algorithm for datatype reasoning. Our algorithm is modular in the sense that it can handle any datatype that supports certain basic operations. We show how to implement these operations for number and string datatypes. 1
The Complexity of Weighted Boolean #CSP with Mixed Signs
, 2009
"... We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set Γ of rational functions, each of which assigns a weight to each variable assignment. Our dichotomy extends previous work ..."
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Cited by 7 (2 self)
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We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set Γ of rational functions, each of which assigns a weight to each variable assignment. Our dichotomy extends previous work in which the weight functions were restricted to being nonnegative. We represent a weight function as a product of the form (−1) s g, where the polynomial s determines the sign of the weight and the nonnegative function g determines its magnitude. We show that the problem of computing the partition function (the sum of the weights of all possible variable assignments) is computable in polynomial time if either every function in Γ can be defined by a “pure affine ” magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of “product type” with a linear sign polynomial. In all other cases, computing the partition function is FP #Pcomplete.
Markov constraints: steerable generation of Markov sequences
, 2010
"... Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as ..."
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Cited by 2 (1 self)
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Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, lefttoright algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domainconsistency for the propagators of EMCs, in an eventbased implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variableorder, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.
Constraint Satisfaction Techniques in Planning and Scheduling
 JOURNAL OF INTELLIGENT MANUFACTURING
"... Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of f ..."
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Cited by 2 (1 self)
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Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of finding a solution to a set of constraints. Planning is the process of finding a sequence of actions that transfer the world from some initial state to a desired state. Scheduling is the problem of assigning a set of tasks to a set of resources subject to a set of constraints. In this paper, we introduce the main definitions and techniques of constraint satisfaction, planning and scheduling from the Artificial Intelligence point of view.
Semiringbased soft constraints
"... Abstract. The semiringbased formalism to model soft constraint has been introduced in 1995 by Ugo Montanari and the authors of this paper. The idea was to make constraint programming more flexible and widely applicable. We also wanted to define the extension via a general formalism, so that all its ..."
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Cited by 1 (1 self)
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Abstract. The semiringbased formalism to model soft constraint has been introduced in 1995 by Ugo Montanari and the authors of this paper. The idea was to make constraint programming more flexible and widely applicable. We also wanted to define the extension via a general formalism, so that all its instances could inherit its properties and be easily compared. Since then, much work has been done to study, extend, and apply this formalism. This papers gives a brief summary of some of these research activities. 1 Before soft constraints: a brief introduction to constraint programming
Insertion Modeling System And Constraint Programming
"... Abstract. The paper relates to practical aspects of insertion modeling. Insertion modeling system is an environment for the development of insertion machines, used to represent insertion models of distributed systems. The architecture of insertion machines and insertion modeling system IMS is presen ..."
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Cited by 1 (1 self)
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Abstract. The paper relates to practical aspects of insertion modeling. Insertion modeling system is an environment for the development of insertion machines, used to represent insertion models of distributed systems. The architecture of insertion machines and insertion modeling system IMS is presented. Insertion machine for constraint programming is specified as an example, and as a starting point of ‘verifiable programming’ project. 1