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Tree Projections: Game Characterization and Computational Aspects

  • Georg Gottlob
  • Gianluigi Greco
  • Zoltán Miklós
  • Francesco Scarcello
  • Thomas Schwentick
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5420)

Abstract

The notion of tree projection provides a natural generalization for various structural decomposition methods, which have been proposed in the literature in order to single out classes of nearly-acyclic (hyper)graphs. In this paper, the mathematical properties of the notion of tree projection are surveyed, and the complexity of the basic tree projection problem (of deciding the existence of a tree projection) is pinpointed. In more details, a game-theoretic characterization (in terms of the Robber and Captain game [15] ) for tree projections is described, which yields a simple argument for the membership in NP of the tree projection problem. Eventually, the main ideas proposed in [14] and underlying the proof of NP-hardness of the tree projection problem are discussed.

Keywords

hypergraphs tree projections computational complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Georg Gottlob
    • 1
  • Gianluigi Greco
    • 2
  • Zoltán Miklós
    • 3
  • Francesco Scarcello
    • 2
  • Thomas Schwentick
    • 4
  1. 1.Oxford UniversityUK
  2. 2.University of CalabriaItaly
  3. 3.École Polytechnique Fédérale de LausanneSwitzerland
  4. 4.Universität DortmundGermany

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