Abstract
Let V be a set of distinct points in some metric space. For each point x ∈ V, 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.
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David Avis and Joe Horton. Remarks on the sphere-of-influence graph. Discrete Geometry and Convexity, 440:323–327, 1985.
Leonidas Guibas, János Pach, and Micha Sharir. Sphere-of-influence graphs in higher dimensions. Colloquia Mathematica Societatis János Bolyai, 63:131–137, 1994.
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© 1998 Springer-Verlag Berlin Heidelberg
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Soss, M. (1998). The Size of the Open Sphere of Influence Graph in L ∞ Metric Spaces. In: Whitesides, S.H. (eds) Graph Drawing. GD 1998. Lecture Notes in Computer Science, vol 1547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37623-2_45
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DOI: https://doi.org/10.1007/3-540-37623-2_45
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