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Exploiting Bounded Treewidth with Datalog (A Survey)

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Datalog Reloaded (Datalog 2.0 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6702))

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Abstract

Many intractable problems have been shown to become tractable if the treewidth of the underlying structure is bounded by a constant. An important tool for deriving such results is Courcelle’s Theorem, which states that all properties definable by Monadic Second Order (MSO) sentences are fixed-parameter tractable with respect to the treewidth. In principle, algorithms can be generated automatically from the MSO definition of a problem by exploiting the correspondence between MSO and finite tree automata (FTA). However, this approach has turned out to be problematic, since even relatively simple MSO formulae may lead to a ”state explosion” of the FTA.

Recently, monadic datalog (i.e., datalog where all intensional predicate symbols are unary) has been proposed as an alternative method to tackle this class of fixed-parameter tractable problems. On the one hand, if some property of finite structures is expressible in MSO then this property can also be expressed by means of a monadic datalog program. Moreover, the resulting fragment of datalog can be evaluated in linear time (both with respect to the program size and with respect to the data size). In this survey, we present the main ideas of this approach and its extension to counting and enumeration problems.

This work was supported by the Austrian Science Fund (FWF), project P20704-N18.

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Authors and Affiliations

  1. Technische Universität Wien, Austria

    Reinhard Pichler

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  1. Reinhard Pichler
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Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Oege de Moor

  2. Department of Computer Science, University of Oxford, UK

    Georg Gottlob , Tim Furche  & Andrew Sellers ,  & 

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Pichler, R. (2011). Exploiting Bounded Treewidth with Datalog (A Survey). In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds) Datalog Reloaded. Datalog 2.0 2010. Lecture Notes in Computer Science, vol 6702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24206-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-24206-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24205-2

  • Online ISBN: 978-3-642-24206-9

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