On the distribution of typical shortest-path lengths in connected random geometric graphs View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2012-06

AUTHORS

D. Neuhäuser, C. Hirsch, C. Gloaguen, V. Schmidt

ABSTRACT

Stationary point processes in ℝ2 with two different types of points, say H and L, are considered where the points are located on the edge set G of a random geometric graph, which is assumed to be stationary and connected. Examples include the classical Poisson–Voronoi tessellation with bounded and convex cells, aggregate Voronoi tessellations induced by two (or more) independent Poisson processes whose cells can be nonconvex, and so-called β-skeletons being subgraphs of Poisson–Delaunay triangulations. The length of the shortest path along G from a point of type H to its closest neighbor of type L is investigated. Two different meanings of “closeness” are considered: either with respect to the Euclidean distance (e-closeness) or in a graph-theoretic sense, i.e., along the edges of G (g-closeness). For both scenarios, comparability and monotonicity properties of the corresponding typical shortest-path lengths Ce∗ and Cg∗ are analyzed. Furthermore, extending the results which have recently been derived for Ce∗, we show that the distribution of Cg∗ converges to simple parametric limit distributions if the edge set G becomes unboundedly sparse or dense, i.e., a scaling factor κ converges to zero and infinity, respectively. More... »

PAGES

199-220

References to SciGraph publications

  • 1977. Processus ponctuels in ECOLE D’ETÉ DE PROBABILITÉS DE SAINT-FLOUR VI-1976
  • 2001-10. Aggregate and fractal tessellations in PROBABILITY THEORY AND RELATED FIELDS
  • 2011-02. Parametric distributions of connection lengths for the efficient analysis of fixed access networks in ANNALS OF TELECOMMUNICATIONS
  • 2002. On the Spanning Ratio of Gabriel Graphs and β-skeletons in LATIN 2002: THEORETICAL INFORMATICS
  • 2008. Stochastic and Integral Geometry in NONE
  • Journal

    TITLE

    Queueing Systems

    ISSUE

    1-2

    VOLUME

    71

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11134-012-9276-z

    DOI

    http://dx.doi.org/10.1007/s11134-012-9276-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1001277440


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    134 https://www.grid.ac/institutes/grid.89485.38 schema:alternateName Orange (France)
    135 schema:name Orange Labs, 38-40, rue du Général Leclerc, 92794, Issy-les-Moulineaux, France
    136 rdf:type schema:Organization
     




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