[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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;
[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] 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.