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SIAM Journal on Computing
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ACM Transactions on Graphics (TOG)
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Communications of the ACM
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ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
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ACM Transactions on Graphics (TOG)
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ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
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ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
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IEEE Transactions on Visualization and Computer Graphics
The four-level nested model revisited: blocks and guidelines
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Proceedings of the 31st ACM international conference on Design of communication
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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. © 2012 Wiley Periodicals, Inc.