Generating labeled planar graphs uniformly at random

Authors:
Manuel Bodirsky;Clemens Gröpl;Mihyun Kang
Affiliations:
Humboldt-Universität zu Berlin, Institut für Informatik, Abteilung Algorithmen und Komplexität I, Unter den Linden 6, 10099 Berlin, Germany;Freie Universität Berlin, Institut für Informatik, Algorithmische Bioinformatik, Takustraβe 9, 14195 Berlin, Germany;Humboldt-Universität zu Berlin, Institut für Informatik, Abteilung Algorithmen und Komplexität I, Unter den Linden 6, 10099 Berlin, Germany
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We present a deterministic polynomial time algorithm to sample a labeled planar graph uniformly at random. Our approach uses recursive formulae for the exact number of labeled planar graphs with n vertices and m edges, based on a decomposition into 1-, 2-, and 3-connected components. We can then use known sampling algorithms and counting formulae for 3-connected planar graphs.