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International Journal of Information Technology & Computer Science ( IJITCS )

Abstract :

The sphere of influence graph of a set of points in the plane is a graph G(V, E) in which the vertex set V consists of the points, and the edge set E consists of edges joining two points if their nearest neighbor circles intersect. The nearest neighbor circle of a point P is the largest circle centered at P that does not contain any other points in its interior. This graph was proposed in 1980 as a geometric model for a primal sketch in computer vision. Since then it has been explored, generalized, and applied to problems in several disciplines. This paper traces the history of this graph, surveys the progress made since 1980, and lists areas for further research.

Keywords :

:sphere of influence graph; proximity graph; intersection graph; graph theory; computational geometry, computer vision, artificial intelligence

References :

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