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Mixing Times of Markov Chains of 2-Orientations

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Book cover WALCOM: Algorithms and Computation (WALCOM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9627))

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Abstract

We study Markov chains for \(\alpha \)-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given function \(\alpha \). The set of \(\alpha \)-orientations of a plane graph has a natural distributive lattice structure. The moves of the up-down Markov chain on this distributive lattice corresponds to reversals of directed facial cycles in the \(\alpha \)-orientation.

A 2-orientation of a plane quadrangulation is an orientation where every inner vertex has outdegree 2. We show that there is a class of plane quadrangulations such that the up-down Markov chain on the 2-orientations of these quadrangulations is slowly mixing. On the other hand the chain is rapidly mixing on 2-orientations of quadrangulations with maximum degree at most 4.

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Authors and Affiliations

  1. Institut Für Mathematik, Technische Universität Berlin, Berlin, Germany

    Stefan Felsner & Daniel Heldt

Authors
  1. Stefan Felsner
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  2. Daniel Heldt
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Correspondence to Stefan Felsner .

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Editors and Affiliations

  1. Dept. of Computer Science and Engin., Bangladesh Univ. of Engin. & Technol., Dhaka, Bangladesh

    Mohammad Kaykobad

  2. Dept. of Computer Science, Sapienza University of Rome, Rome, Italy

    Rossella Petreschi

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Felsner, S., Heldt, D. (2016). Mixing Times of Markov Chains of 2-Orientations. In: Kaykobad, M., Petreschi, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2016. Lecture Notes in Computer Science(), vol 9627. Springer, Cham. https://doi.org/10.1007/978-3-319-30139-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-30139-6_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30138-9

  • Online ISBN: 978-3-319-30139-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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