Linear Orderings of Random Geometric Graphs

  • Josep Díaz
  • Mathew D. Penrose
  • Jordi Petit
  • María Serna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1665)


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.


Linear Ordering Random Graph Layout Problem Geometric Graph Grid Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Josep Díaz
    • 1
  • Mathew D. Penrose
    • 2
  • Jordi Petit
    • 1
  • María Serna
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of Mathematical SciencesUniversity of DurhamDurhamEngland

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