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Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth

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Book cover Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

We study the complexity of several of the classical graph decision problems in the setting of bounded cutwidth and how imposing planarity affects the complexity. We show that for 2-coloring, for bipartite perfect matching, and for several variants of disjoint paths, the straightforward NC 1 upper bound may be improved to AC 0[2], ACC 0, and AC 0 respectively for bounded planar cutwidth graphs. We obtain our upper bounds using the characterization of these circuit classes in tems of finite monoids due to Barrington and Thérien. On the other hand we show that 3-coloring and Hamilton cycle remain hard for NC 1 under projection reductions, analogous to the NP-completeness for general planar graphs. We also show that 2-coloring and (non-bipartite) perfect matching are hard under projection reductions for certain subclasses of AC 0[2]. In particular this shows that our bounds for 2-coloring are quite close.

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Authors and Affiliations

  1. Aarhus University, Denmark

    Kristoffer Arnsfelt Hansen, Sven Skyum & Navid Talebanfard

  2. IIT Madras, Chennai, India

    Balagopal Komarath & Jayalal Sarma

Authors
  1. Kristoffer Arnsfelt Hansen
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  2. Balagopal Komarath
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  3. Jayalal Sarma
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  4. Sven Skyum
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  5. Navid Talebanfard
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Hansen, K.A., Komarath, B., Sarma, J., Skyum, S., Talebanfard, N. (2014). Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_29

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  • DOI: https://doi.org/10.1007/978-3-662-44465-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

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