Abstract
β-skeletons, a prominent member of the neighborhood graph family, have interesting geometric properties and various applications ranging from geographic networks to archeology. This paper focuses on computing the β-spectrum, a labeling of the edges of the Delaunay Triangulation, DT(V), which makes it possible to quickly find the lune-based β-skeleton of V for any query value β ∈ [1, 2]. We consider planar n point sets V with L p metric, 1 < p < ∞. We present a O(n log2 n) time sequential, and a O(log4 n) time parallel β-spectrum labeling. We also show a parallel algorithm, which for a given β ∈ [1,2], finds the lune-based β-skeleton in O(log2 n) time. The parallel algorithms use O(n) processors in the CREW-PRAM model.
This research is supported by the ESF EUROCORES programme EUROGIGA, CRP VORONOI.
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Kowaluk, M., Majewska, G. (2013). New Sequential and Parallel Algorithms for Computing the β-Spectrum. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_21
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DOI: https://doi.org/10.1007/978-3-642-40164-0_21
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