Abstract
The β-skeleton is a measure of the internal shape of a planar set of points. We get an entire spectrum of shapes by varying the parameter β. For a fixed value of β, a β-skeleton is a geometric graph obtained by joining each pair of points whose β-neighborhood is empty.
For β≥1, this neighborhood of a pair of points p i ,p j is the interior of the intersection of two circles of radius , centered at the points (1−β/2)p i +(β/2)p j and (β/2)p i +(1−β/2)p j , respectively. For β∈(0,1], it is the interior of the intersection of two circles of radius , passing through p i and p j .
In this paper we present an output-sensitive algorithm for computing a β-skeleton in the metrics l 1 and l ∞ for any β≥2. This algorithm is in O(nlogn+k), where k is size of the output graph. The complexity of the previous best known algorithm is in O(n 5/2logn) [7].
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Received April 26, 2000
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Mukhopadhyay, A., Rao, S. Output-Sensitive Algorithm for Computing β-Skeletons. Computing 65, 285–289 (2000). https://doi.org/10.1007/s006070070013
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DOI: https://doi.org/10.1007/s006070070013