286 research outputs found

    Tractable constraints on ordered domains

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    AbstractFinding solutions to a constraint satisfaction problem is known to be an NP-complete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. In this paper we identify a restricted set of contraints which gives rise to a class of tractable problems. This class generalizes the notion of a Horn formula in propositional logic to larger domain sizes. We give a polynomial time algorithm for solving such problems, and prove that the class of problems generated by any larger set of constraints is NP-complete

    Movies in the classroom: lessons for curriculum design

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    There is a burgeoning body of literature (Johnson and Jackson 2005; Cornett, 2006; Jensen and Curtis, 2008; Smith, 2009; Edwards et al, 2015) which suggests that, by incorporating into our teaching the humanities, including film, we can enhance the learning experience of our students and help lay the foundations for greater sensitivity, understanding and empathy, as well as make the learning more ‘real’

    The power of propagation:when GAC is enough

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    Considerable effort in constraint programming has focused on the development of efficient propagators for individual constraints. In this paper, we consider the combined power of such propagators when applied to collections of more than one constraint. In particular we identify classes of constraint problems where such propagators can decide the existence of a solution on their own, without the need for any additional search. Sporadic examples of such classes have previously been identified, including classes based on restricting the structure of the problem, restricting the constraint types, and some hybrid examples. However, there has previously been no unifying approach which characterises all of these classes: structural, language-based and hybrid. In this paper we develop such a unifying approach and embed all the known classes into a common framework. We then use this framework to identify a further class of problems that can be solved by propagation alone

    A Graph Based Backtracking Algorithm for Solving General CSPs

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    Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches

    Complexity of Discrete Energy Minimization Problems

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    Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

    Non-Local Configuration of Component Interfaces by Constraint Satisfaction

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    © 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s10601-020-09309-y.Service-oriented computing is the paradigm that utilises services as fundamental elements for developing applications. Service composition, where data consistency becomes especially important, is still a key challenge for service-oriented computing. We maintain that there is one aspect of Web service communication on the data conformance side that has so far escaped the researchers attention. Aggregation of networked services gives rise to long pipelines, or quasi-pipeline structures, where there is a profitable form of inheritance called flow inheritance. In its presence, interface reconciliation ceases to be a local procedure, and hence it requires distributed constraint satisfaction of a special kind. We propose a constraint language for this, and present a solver which implements it. In addition, our approach provides a binding between the language and C++, whereby the assignment to the variables found by the solver is automatically translated into a transformation of C++ code. This makes the C++ Web service context compliant without any further communication. Besides, it uniquely permits a very high degree of flexibility of a C++ coded Web service without making public any part of its source code.Peer reviewe

    Tractability in Constraint Satisfaction Problems: A Survey

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    International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP

    The Diversity of Religious Diversity. Using Census and NCS Methodology in Order to Map and Assess the Religious Diversity of a Whole Country

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    Religious diversity is often captured in “mapping studies” that use mostly qualitative methods in order to map and assess the religious communities in a given area. While these studies are useful, they often present weaknesses in that they treat only limited geographic regions, provide limited possibilities for comparing across religious groups and cannot test theories. In this article, we show how a census and a quantitative national congregations study (NCS) methodology can be combined in order to map and assess the religious diversity of a whole country (Switzerland), overcoming the problems mentioned above. We outline the methodological steps and selected results concerning organizational, geographic, structural, and cultural diversity
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