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In this paper, we investigate the complexity of algorithms for solving CSPs which are classically implemented in real practical solvers, such as Forward Checking or Bactracking with Arc Consistency (RFL or MAC).. We introduce a new parameter for measuring their complexity and then we derive new complexity bounds. By relating the complexity of CSP algorithms… (More)

Find new islands of tractability, that is classes of CSP instances for which polytime algorithms exist, is a fundamental task in the study of constraint satisfaction problems. The concept of hybrid tractable class, which allows to deal simultaneously with the restrictions of languages and, for example, the satisfaction of structural properties, is an… (More)

The question of tractable classes of constraint satisfaction problems (CSPs) has been studied for a long time, and is now a very active research domain. However, studies of tractable classes are typically very theoretical. They usually introduce classes of instances together with polynomial time algorithms for recognizing and solving them, and the… (More)

A binary CSP instance satisfying the broken-triangle property (BTP) can be solved in polynomial time. Unfortunately, in practice, few instances satisfy the BTP. We show that a local version of the BTP allows the merging of domain values in arbitrary instances of binary CSP, thus providing a novel polynomial-time reduction operation. Extensive experimental… (More)

Many works have studied the properties of CSPs which are based on the structures of constraint networks, or based on the features of compatibility relations. Studies on structures rely generally on properties of graphs for binary CSPs and on properties of hypergraphs for the general case, that is CSPs with constraints of arbitrary arity. In the second case,… (More)

The CSP formalism has shown, for many years, its interest for the representation of numerous kinds of problems, and also often provide effective resolution methods in practice. This formalism has also provided a useful framework for the knowledge representation as well as to implement efficient methods for reasoning about knowledge. The data of a CSP are… (More)

—Tractable classes constitute an important issue in CP, at least from a theoretical viewpoint. But they are not actually used in practice. Either their treatment is too costly for time complexity or, even if there exist efficient algorithms to manage them, they do not appear in the real problems. We propose here to address this issue thanks to the notion of… (More)

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