The Size of the Open Sphere of Influence Graph in L Metric Spaces

  • Michael Soss
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


Let V be a set of distinct points in some metric space. For each point xV, let r x be the distance from x to its nearest neighbour, and let s x be the open ball centered at x with radius equal to the distance from x to its nearest neighbour. We refer to these balls as the spheres of influence of the set V. The open sphere of influence graph on V is defined as the graph where (x,y) is an edge if and only if s x and s y intersect.


  1. [1]
    David Avis and Joe Horton. Remarks on the sphere-of-influence graph. Discrete Geometry and Convexity, 440:323–327, 1985.MathSciNetGoogle Scholar
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    Leonidas Guibas, János Pach, and Micha Sharir. Sphere-of-influence graphs in higher dimensions. Colloquia Mathematica Societatis János Bolyai, 63:131–137, 1994.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Michael Soss
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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