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Deciding First Order Properties of Matroids

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Automata, Languages, and Programming (ICALP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7392))

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Abstract

Frick and Grohe [J. ACM 48 (2006), 1184–1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order property can be decided in almost linear time in such a graph class. Here, we introduce an analogous notion for matroids (locally bounded branch-width) and show the existence of a fixed parameter algorithm for first order properties in classes of regular matroids with locally bounded branch-width. To obtain this result, we show that the problem of deciding the existence of a circuit of length at most k containing two given elements is fixed parameter tractable for regular matroids.

A full version of this contribution is available as arXiv:1108.5457.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague, Czech Republic

    Tomáš Gavenčiak

  2. Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14, Pilsen, Czech Republic

    Daniel Král

  3. Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague, Czech Republic

    Daniel Král

  4. Department of Mathematical Sciences, KAIST, 291 Daehak-ro Yuseong-gu, Daejeon, 305-701, South Korea

    Sang-il Oum

Authors
  1. Tomáš Gavenčiak
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  2. Daniel Král
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  3. Sang-il Oum
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Centre for Discrete Mathematics and its Applications, University of Warwick, Warwick, UK

    Artur Czumaj

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Kurt Mehlhorn

  3. Computer Laboratory,, University of Cambridge, UK

    Andrew Pitts

  4. ETH Zurich, Switzerland

    Roger Wattenhofer

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Gavenčiak, T., Král, D., Oum, Si. (2012). Deciding First Order Properties of Matroids. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-31585-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31584-8

  • Online ISBN: 978-3-642-31585-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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