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Exact and Efficient Generation of Geometric Random Variates and Random Graphs

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

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Abstract

The standard algorithm for fast generation of Erdős-Rényi random graphs only works in the Real RAM model. The critical point is the generation of geometric random variates Geo(p), for which there is no algorithm that is both exact and efficient in any bounded precision machine model. For a RAM model with word size w = Ω(loglog(1/p)), we show that this is possible and present an exact algorithm for sampling Geo(p) in optimal expected time \(\mathcal{O}(1 + \log(1/p) / w)\). We also give an exact algorithm for sampling min{n, Geo(p)} in optimal expected time \(\mathcal{O}(1 + \log(\operatorname{min}\{1/p,n\})/w)\). This yields a new exact algorithm for sampling Erdős-Rényi and Chung-Lu random graphs of n vertices and m (expected) edges in optimal expected runtime \(\mathcal{O}(n + m)\) on a RAM with word size w = Θ(logn).

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Author information

Authors and Affiliations

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

    Karl Bringmann

  2. Friedrich-Schiller-Universität Jena, Germany

    Tobias Friedrich

Authors
  1. Karl Bringmann
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  2. Tobias Friedrich
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

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

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Bringmann, K., Friedrich, T. (2013). Exact and Efficient Generation of Geometric Random Variates and Random Graphs. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_23

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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