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Tree Projections: Hypergraph Games and Minimality

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Automata, Languages and Programming (ICALP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5125))

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Abstract

A hypergraph-game characterization is provided for hypergraph tree projections (TPs) and, hence, for the special cases of generalized and fractional hypertree decompositions, where such a characterization was missing and asked for. In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones, which are yet somehow preferable, because they correspond to minimal tree projections. In fact, it is shown that minimal TPs enjoy a number of nice properties, such as the same kind of connection property as (minimal) tree decompositions of graphs. Finally, it is shown that this property is somehow tight, by giving a negative answer to an open question about a slightly stronger notion of connection property, defined to speed-up the computation of hypertree decompositions.

This work was partially supported by M.I.U.R. under project TOCAI.IT, and by the Institute for High Performance Computing and Networks (ICAR-CNR) under project ICT.P09.001.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, UNICAL, Via P. Bucci 30B, 87036, Rende, Italy

    Gianluigi Greco

  2. DEIS, UNICAL, Via P. Bucci 30B, 87036, Rende, Italy

    Francesco Scarcello

Authors
  1. Gianluigi Greco
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  2. Francesco Scarcello
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Editor information

Editors and Affiliations

  1. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Luca Aceto

  2. Department of Computer Science, IT-Parken, University of Aarhus, Ã…bogade 34, 8200, Ã…rhusN, Denmark

    Ivan Damgård

  3. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  4. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavik, Iceland

    Magnús M. Halldórsson

  5. Department of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Anna Ingólfsdóttir

  6. Université de Bordeaux-1, LaBRI, 351, Cours de la Libération, 33405, Talence cedex, France

    Igor Walukiewicz

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© 2008 Springer-Verlag Berlin Heidelberg

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Greco, G., Scarcello, F. (2008). Tree Projections: Hypergraph Games and Minimality. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_60

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  • DOI: https://doi.org/10.1007/978-3-540-70575-8_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70574-1

  • Online ISBN: 978-3-540-70575-8

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