Different Classes of Graphs to Represent Microstructures for CSPs View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2014

AUTHORS

Achref El Mouelhi , Philippe Jégou , Cyril Terrioux

ABSTRACT

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 usually expressed in terms of a constraint network. This network is a (constraints) graph when the arity of the constraints is equal to two (binary constraints), or a (constraint) hypergraph in the case of constraints of arbitrary arity, which is generally the case for problems of real life. The study of the structural properties of these networks has made it possible to highlight certain properties, which led to the definition of new tractable classes, but in most cases, they have been defined for the restricted case of binary constraints. So, several representations by graphs have been proposed for the study of constraint hypergraphs to extend the known results to the binary case. Another approach, finer, is interested in the study of the microstructure of CSP, which is defined by graphs. This helped, offering a new theoretical framework to propose other tractable classes. In this paper, we propose to extend the notion of microstructure to any type of CSP. For this, we propose three kinds of graphs that can take into account the constraints of arbitrary arity. We show how these new theoretical tools can already provide a framework for developing new tractable classes for CSPs. We think that these new representations should be of interest for the community, firstly for the generalization of existing results, but also to obtain original results. More... »

PAGES

21-38

References to SciGraph publications

  • 1988. Tree Search and ARC Consistency in Constraint Satisfaction Algorithms in SEARCH IN ARTIFICIAL INTELLIGENCE
  • 2003. Improved Algorithms for Counting Solutions in Constraint Satisfaction Problems in PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING – CP 2003
  • 2008. Perfect Constraints Are Tractable in PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
  • 2009-12. On implementing symmetry detection in CONSTRAINTS
  • 2006-07. Symmetry Definitions for Constraint Satisfaction Problems in CONSTRAINTS
  • 2013. Some New Tractable Classes of CSPs and Their Relations with Backtracking Algorithms in INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS
  • 2003. A New Class of Binary CSPs for which Arc-Consistency Is a Decision Procedure in PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING – CP 2003
  • Book

    TITLE

    Graph Structures for Knowledge Representation and Reasoning

    ISBN

    978-3-319-04533-7
    978-3-319-04534-4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-04534-4_3

    DOI

    http://dx.doi.org/10.1007/978-3-319-04534-4_3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1032420536


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