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KOPS - The Institutional Repository of the University of Konstanz, 2012
Published in:Computer Graphics Forum. 2012, 31(3pt1), pp. 855-864. ISSN 0167-7055. eISSN 1467-8659. Available under: doi:10.1111/j.1467-8659.2012.03078.x
Footnote:
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Description:
Voronoi treemaps represent hierarchies as nested polygons. We here show that, contrary to the apparent popular belief, utilization of an algorithm for weighted Voronoi diagrams is not only feasible, but also more efficient than previous low-resolution approximations, even when the latter are implemented on graphics hardware. More precisely, we propose an instantiation of Lloyd's method for centroidal Voronoi diagrams with Aurenhammer's algorithm for power diagrams that yields an algorithm running in O(n log n) rather than Ω(n²) time per iteration, with n the number of sites. We describe its implementation and present evidence that it is faster also in practice. ; published