Evgenij Thorstensen

University of Oxford, Oxford, England, United Kingdom

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Publications (6)0 Total impact

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    ABSTRACT: We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.
    07/2013;
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    Evgenij Thorstensen
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    ABSTRACT: A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP instances that yield tractable classes have been identified. However, many such restrictions fail to guarantee tractability for CSPs with global constraints. In this paper, we investigate the properties of extensionally represented constraints that these restrictions exploit to achieve tractability, and show that there are large classes of global constraints that also possess these properties. This allows us to lift these restrictions to the global case, and identify new tractable classes of CSPs with global constraints.
    07/2013;
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    ABSTRACT: This paper reviews structural problem decomposition methods, such as tree and path decompositions. It is argued that these notions can be applied in two distinct ways: Either to show that a problem is efficiently solvable when a width parameter is fixed, or to prove that the unrestricted (or some width-parameter free) version of a problem is tractable by using a width-notion as a mathematical tool for directly solving the problem at hand. Examples are given for both cases. As a new showcase for the latter usage, we report some recent results on the Partner Units Problem, a form of configuration problem arising in an industrial context. We use the notion of a path decomposition to identify and solve a tractable class of instances of this problem with practical relevance.
    Symposium on Theoretical Aspects of Computer Science (STACS2011). 01/2011;
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    ABSTRACT: In this work we present the Partner Units Problem as a novel challenge for optimization methods. It captures a certain type of configuration problem that frequently occurs in industry. Unfortunately, it can be shown that in the most general case an optimization version of the problem is intractable. We present and evaluate encodings of the problem in the frameworks of answer set programming, propositional satisfiability testing, constraint solving, and integer programming. We also show how to adapt these encodings to a class of problem instances that we have recently shown to be tractable.
    Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems - 8th International Conference, CPAIOR 2011, Berlin, Germany, May 23-27, 2011. Proceedings; 01/2011
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    ABSTRACT: The Partner Units Problem is a specific type of configuration problem with important applications in the area of surveillance and security. In this work we show that a special case of the problem, that is of great interest to our partners in industry, can directly be tackled via a structural problem decompostion method. Combining these theoretical insights with general purpose AI techniques such as constraint satisfaction and SAT solving proves to be particularly effective in practice.
    IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16-22, 2011; 01/2011
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    Peter Baumgartner, Evgenij Thorstensen
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    ABSTRACT: Instance-based methods are a specific class of methods for automated proof search in first-order logic. This article provides an overview of the major methods in the area and discusses their properties and relations to the more established resolution methods. It also discusses some recent trends on refinements and applications. This overview is rather brief and informal, but we provide a comprehensive literature list to follow-up on the details.
    24(1):35-42.