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Linear Orderings of Random Geometric Graphs

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Graph-Theoretic Concepts in Computer Science (WG 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

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Abstract

In random geometric graphs, vertices are randomly distributed on [0, 1]2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.

This research was partially supported by ESPRIT LTR Project no. 20244 — ALCOM-IT, CICYT Project TIC97-1475-CE, and CIRIT project 1997SGR-00366.

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Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord C6. Jordi Girona 1-3, 08034, Barcelona, Spain

    Josep Díaz, Jordi Petit & María Serna

  2. Department of Mathematical Sciences, University of Durham, South Road, Durham, DH1 3LE, England

    Mathew D. Penrose

Authors
  1. Josep Díaz
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  2. Mathew D. Penrose
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  3. Jordi Petit
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  4. María Serna
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Díaz, J., Penrose, M.D., Petit, J., Serna, M. (1999). Linear Orderings of Random Geometric Graphs. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_28

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  • DOI: https://doi.org/10.1007/3-540-46784-X_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

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