Abstract
Given a set of n points in the plane, any β-skeleton and [γtO,γ1] graph can be computed in quadratic time. The presented algorithms are optimal for β values that are less than 1 and [γtO,γ1] values that result in non-planar graphs. For β = 1, we show a numerically robust algorithm that computes Gabriel graphs in quadratic time and degree 2. We finally show how a β-spectrum can be computed in optimal O(n 2) time. Research supported in part by the CNR Project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed al CAD”, the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%), by Gen. Cat. SGR000356 and MEC-DGES-SEUID PB98-0933, Spain, and by NSERC, Canada.
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Hurtado, F., Liotta, G., Meijer, H. (2001). Optimal, Suboptimal, and Robust Algorithms for Proximity Graphs. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_2
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DOI: https://doi.org/10.1007/3-540-44634-6_2
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