Partitioning of complex scenes of geometric objects
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We are concerned with the problem of partitioning complex scenes of geometric objects in order to support the solutions of proximity problems. We present a data structure called Monotonous Bisector* Tree, which can be regarded as a divisive hierarchical approach of centralized clustering methods (compare  and ). We analyze some structural properties showing that Monotonous Bisector* Trees are a proper tool for the representation of proximity information in complex scenes of geometric objects, even in general metric spaces.
Given a scene of n convex objects in d-dimensional space and a L p -metric. We show that a Monotonous Bisector* Tree with logarithmic height can be constructed in optimal O(n log n) time using O(n) space. This statement still holds if we demand that the cluster radii, which appear on a path from the root down to a leaf, should generate a geometrically decreasing sequence.
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