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Representing CSPs with Set-Labeled Diagrams: A Compilation Map

  • Alexandre Niveau
  • Hélène Fargier
  • Cédric Pralet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7205)

Abstract

Constraint Satisfaction Problems (CSPs) offer a powerful framework for representing a great variety of problems. Unfortunately, most of the operations associated with CSPs are NP-hard. As some of these operations must be addressed online, compilation structures for CSPs have been proposed, e.g. finite-state automata and Multivalued Decision Diagrams (MDDs).

The aim of this paper is to draw a compilation map of these structures. We cast all of them as fragments of a more general framework that we call Set-labeled Diagrams (SDs), as they are rooted, directed acyclic graphs with variable-labeled nodes and set-labeled edges; contrary to MDDs and Binary Decision Diagrams, SDs are not required to be deterministic (the sets labeling the edges going out of a node are not necessarily disjoint), ordered nor even read-once.

We study the relative succinctness of different subclasses of SDs, as well as the complexity of classically considered queries and transformations. We show that a particular subset of SDs, satisfying a focusing property, has theoretical capabilities very close to those of Decomposable Negation Normal Forms (DNNFs), although they do not satisfy the decomposability property stricto sensu.

Keywords

Model Check Variable Order Constraint Satisfaction Problem Outgoing Edge Label Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexandre Niveau
    • 1
  • Hélène Fargier
    • 2
  • Cédric Pralet
    • 3
  1. 1.CRIL/Université d’ArtoisLensFrance
  2. 2.IRIT/CNRSToulouseFrance
  3. 3.Onera/DCSDToulouseFrance

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